On the radio the other day, a consumer adviser told listeners to invest in insured institutions. But if you can't, the voice said, make sure that the uninsured business is being conducted on a "sound basis."

Never mind the impracticality of the advice. (How could the average investor determine whether a business operation is sound?) The revealing underlying assumption was that if an institution is insured, one needn't question whether it's sound or unsound.

In a deregulated world, that psychology is precisely what encouraged many banks and savings and loan associations, competing for the consumer dollar, to take risks they would otherwise have found unacceptable.

Now there is a time bomb ticking away: the federal deposit insurance system may not be able to cope with potential runs on these institutions. There are hundreds of sick S&Ls shored up by the Federal Savings and Loan Insurance Corp. It provides depositors with federal insurance up to $100,000 in the same way that the Federal Deposit Insurance Corp. insures deposits at commercial banks.

On a realistic accounting basis, many S&Ls would in fact be bankrupt because of their bad investments, notably in real estate. Because the cost of covering all potential losses far exceeds the FSLIC insurance fund of less than $4 billion, regulatory officials are talking of setting up a new agency empowered to borrow as much as $20 billion in private markets to augment the FSLIC's bail-out funds.

Another possible "solution" is a merger of the FSLIC into the FDIC, which would have the practical effect of wiping out the distinction between thrifts and banks. The FDIC is in a stronger position than the FSLIC. Nonetheless, it begins to appear that a merger would be a case of the halt aiding the blind.

A revealing new book, "The Gathering Crisis in Federal Deposit Insurance," by Ohio State University Prof. Edward J. Kane, says we have been lulled into thinking the FDIC and FSLIC provide a cheap, logical way of ensuring that the corner bank or S&L will be stable -- or you can get your money back.

Kane has a gift for simple metaphor that brings the problem to life. He likens the fragility of the deposit-insurance system -- one of the remaining legacies of the New Deal -- to an old car that hasn't been well maintained. While still adequate for "light loads in flat country, it cannot be driven endlessly up and down steep interest-rate mountains without breaking down," he says.

"There is good reason to doubt either that the old car has many more interest-rate mountains left in it, or that it can be steered unharmed through the mine field of contemporary financial services competition."

At present, some 900 of the nation's 14,700 banks are on a "problem" list. That means, according to the FDIC rating system, that they run a significant risk of failure. The FSLIC doesn't even admit that it keeps a list, acknowledging only that 73 S&Ls disappeared last year, while 672 vanished in 1982 and 1983. The last time I mentioned these numbers, an FSLIC official protested to The Post that the public was being unnecessarily frightened by exaggerations.

Writes Kane: "The point that authorities don't want to face is that, however well the deposit-insurance system may have run in the past, it is headed for a bureaucratic breakdown. . . . Unless market discipline is reimposed on deposit institution risk-taking, the deposit-insurance bureaucracy will seize up at a most inopportune time."

Kane argues for dramatic changes -- "trading in" the old deposit insurance "jalopy" before it cracks up with its passengers aboard. His "new model" would be one with reduced coverages and increased fees designed to force managers to make safer investments. He would gradually lower the basic insurance limit to $10,000 (then index it for inflation). Larger balances, in successive $10,000 slices, would be available at an increased insurance cost, to be paid for by the institutions or the depositors.

He believes Congress made a big mistake in 1980 when it boosted the insured account limit to $100,000. That was much more than the average householder needed, but in effect it enabled the banks to issue federally guaranteed debt that was in many ways superior to Treasury debt.

To be sure, a congressional resolution has reaffirmed that "the full faith and credit" of the federal government is behind the FDIC and FSLIC. That may guarantee savers against long-term losses, while the taxpayers pick up the check. But the resolution doesn't say just how it would work, or ensure that there won't be some panic while Congress acts to fulfill its promise.

Kane's proposals may e difficult for politicians to swallow. But his diagnosis of the problem rings true, and he makes a compelling case that the existing insurance system has been pushed beyond its capacity.