The recovery may be just around the corner, as President Reagan says. But the pain and suffering at many companies will linger long after the economy starts to improve, and far longer than in earlier recoveries.

Some corporations are so far in debt that they may not be able to take full advantage of the normal upswing in demand that follows the end of an economic slide. As a result, the recovery itself may be weaker and shorter and less beneficial to workers and companies alike.

Many companies will pay the price for operating as if inflation would never end. These are the companies that borrowed heavily to expand--counting on buying appreciating assets with depreciating dollars and passing along heady interest costs in higher prices. The value of those assets are not rising very fast as inflation subsides. But interest rates, although lower than a year ago, remain high; while consumer price inflation is running between 6 percent and 7 percent, the prime rate is 16 1/2 percent.

As a result, the companies are saddled with short-term debt (loans that must be paid off or refinanced within a year or less) that they cannot pay off or convert to long-term debt. Meanwhile, profits have deteriorated sharply and bankruptcies are more numerous than at any time in the post-war period.

Spectacular failures, such as Braniff International's last week, could come more frequently unless interest rates soon subside.

"Corporations today have the worst liquidity cash position and liability structure in the entire post-war period," says Henry Kaufman, chief economist for Salomon Brothers Inc.

By the end of most previous recessions, companies had shed much of their short-term debt. As prices and interest rates declined, and short-term rates fell below long-term rates, investors were willing to lend for longer periods of time. Companies then sold long-term, more secure debts such as bonds and used the proceeds to pay off their banks. When orders started to rise, companies borrowed short-term again to finance an increase in inventories and provide cash flow.

But in this recession interest rates have remained high; investors, apparently fearing a resurgence in inflation, are reluctant to commit funds to long-term loans, and the bond market is moribund.

Thus many companies that normally would be selling bonds are still trying to get short-term loans from bankers.

"The credit situation is more worrisome than at any time in the post-war period," Kaufman says.

In the first four months of 1982, companies borrowed $18 billion from their bankers. During the same period in 1981, net corporate borrowing totaled $4.5 billion, according to Kaufman. Meanwhile, new corporate bond offerings have averaged $1.5 billion a month, compared with $3 billion a month in 1981, a year that was considered difficult for long-term debt offerings.

The higher a company's short-term debt load, the more vulnerable it is to increases in interest rates or to a sudden change in the business climate that makes lenders leery. The money a company raises in a 15-year bond is secure for 15 years. The money it raises from a bank might have to be repaid in 90 days. Commercial paper (essentially a corporate IOU) might have to be paid back within eight days. If bankers or buyers of commercial paper get cold feet--frightened, perhaps, by an unexpected major corporate failure--companies depending on short-term loans could face big trouble.

To lighten its need for short-term debt as profits slow during a recession, business lays off workers, cuts other costs and slashes inventories. Companies have taken those steps in this recession--at 9.4 percent and headed higher, the unemployment rate is at a post-war peak, and inventories are cut to the bone. "But the amalgam of short-term debt keeps piling up," according to Edward Yardeni, chief economist for the brokerage firm E.F. Hutton & Co.

Because many businesses have more short-term debt than they consider desirable and banks are strapped for funds, businesses run the risk of being unable to get the funds needed to finance an upturn in demand that should occur by summer, when the next round of income tax cuts take effect.

"Even if interest rates decline, businesses don't have the financial capability to come back as fast as they did after previous recessions," according to Alan Greenspan, head of the economic consulting firm Townsend-Greenspan and former chairman of the Council of Economic Advisers. Even in the best scenario, Greenspan sees a recovery that is weak. Many economists worry that it will be too weak to sustain itself.

"There are downside risks to the recovery," according to Jack Lavery, chief economist for Merrill Lynch Pierce Fenner & Smith, the nation's biggest brokerage firm.

The biggest risk of all is that interest rates will not fall. If that happens, the wave of business failures and problem loans cascading across the land will grow, Lavery said.

More than 6,200 companies went bankrupt during the first three months of 1982, 55 percent more than during the same period last year. Bankers, already trying to ease debt terms for companies having trouble paying on the original schedule, will spend more time trying to "fix" old loans than make new ones.

Moreover, interest costs are siphoning off an increasing percentage of corporate income, not only reducing the corporate cash cushion, but further dampening an already weak desire to invest in new plants and more modern facilities.

In the first three months of 1982, 42 percent of corporate pre-tax income went to pay off debt, compared with 28 percent in 1979, according to Jerry Jasinowski, chief economist of the National Association of Manufacturers.

Because of the strains on financial balance sheets, credit ratings of many major companies are declining. In the last 16 months, Standard & Poor's has lowered the ratings of more than 150 companies. That makes it harder and more expensive for those companies to borrow.

While a heavy load of short-term debt makes a company vulnerable to sudden changes in the economic climate, those with large amounts of expensive long-term debt feel the cost pressure, too. Republic Airlines, for example, made $5.1 million flying planes in the first quarter but lost $22.5 million overall because of interest costs.

Even many well-managed, relatively healthy companies--especially those in basic industries like steel, automobiles, aluminum and appliances--are chafing under the pressures of falling prices, falling demand, high interest rates and heavier than normal debt loads.

On the whole, however, well-managed large companies, with the exception of savings and loan associations, "are having some problems, but are not up against the wall," according to George Baker, senior executive vice president of Continental Illinois National Bank, the nation's second-biggest commercial lender.

The outlook is the same for smaller businesses, which often have a tougher time than large companies. They have fewer resources to weather bad times, must rely upon banks for most of their credit needs (big companies with good ratings can issue less expensive commercial paper), and have to pay higher interest rates as well.

But small companies will survive if the economy turns up and interest rates turn down.

The current recession, however, has been unforgiving of managements that made mistakes. Too often, companies pushed to the brink greased the skids with an imprudent amount of short-term debt.

Three major recent examples:

International Harvester Co. had a record profit in 1979. But its new chairman, Archie R. McCardell, took a six-month strike; Harvester lost sales and watched its short-term debt balloon from $450 million to $1.1 billion. The strike ended on an inconclusive note in April 1980, but by then, Harvester's major customers--farmers, truckers and construction companies--were in a recession.

Harvester's sales fell and its debt rose to $4.2 billion. Earlier this month McCardell was replaced as chairman. Meanwhile, sales continue to weaken and losses continue to mount. Harvester today is kept from bankruptcy by its bankers' goodwill.

Braniff International Corp., which controlled a profitable airline based in Dallas, decided to expand in the late 1970s. But the route network it created was built on a mound of debt that eventually exceeded $730 million.

Then fuel prices surged in the wake of the Iranian crisis, passenger traffic--and its income--declined because of the recession, and interest costs rose sharply. The air traffic controllers strike put a further crimp in its business. Between 1979 and 1981 its losses totaled $336 million.

Braniff tried to retrench, but too late. Last Thursday it filed for bankruptcy, less than 12 hours after it suspended all flights.

Wickes Cos. was a big housing-related retailer with an urge to acquire. Its last major acquisition, Gamble-Skogmo Inc. in 1980, probably was one too many. Wickes started off a century ago as a small country store and agricultural elevator operator firm in Saginaw, Mich. It added a lumber yard and grew by acquisition into a major furniture, building supplies and lumber operation with thousands of stores worldwide.

But it borrowed a lot to grow--of the $200 million it paid for the Minneapolis retailer Gamble-Skogmo, $125 million came from its bankers. According to Value Line Investment Survey, Wickes has more than $600 million in long-term debt.

In February, owing hundreds of millions of dollars in short-term loans, Wickes negotiated $580 million more from its bankers, to be repaid July 31. When 1982 started Wickes was paying $200 million a year in interest. That cost continued to grow while demand for lumber, housing and furniture continued to slide. Last month Wickes filed for bankruptcy, reporting it owed $2 billion, most to its bankers, but some to suppliers.

There is some ground for optimism in this bleak environment, argues Continental Illinois' Baker, the bank's top lending officer. He says that if Congress and the president reach a budget compromise that lowers the 1983 deficit from the projected $182 billion to about $100 billion and promises smaller deficits in following years, more investors will be willing to lend long-term.

Once investors are convinced that inflation will not be revived, they will be happy to lock in relatively high long-term interest rates. Companies that passed up bond offerings a year or two ago, preferring to borrow short-term and wait for rates to come down, will not make the same mistake again, he believes.

A favorable budget compromise could bring interest rates down 4 percentage points in a matter of weeks, Baker insists. "A vast amount of money" would be available for long-term lending and companies could quickly raise bond funds and pay off their bankers.

But he admits his analysis may be wishful thinking.

Most economists say they don't know what will happen.

Former Economic Council Chairman Greenspan said economists are puzzled because the economy never has been as depressed for so long while interest rates stayed so high and companies continued to pile up massive amounts of short-term debt.

"We have no historical experience to analogize by," Greenspan said.