They remember the second quarter of 1979 with fondness at the company's Philadelphia headquarters. That was the quarter they turned a nifty $23 million profit.

Unfortunately, that was also the only three-month period in its five-year existence in which the company reported any kind of profit. For all 12 months of that year, 1979, its losses were $202 million. In 1978, the company lost $385 million; in 1977 it lost $366 million.

With a record like that, it's fair to ask why the company is still in existence. And the answer is that it's no ordinary business venture. It is Conrail, the offspring of the Penn Central and six other bankrupt railroads that was established by the federal government five years ago to preserve railroad freight service in the Northeast and Midwest.

That has turned out to be an expensive proposition for the federal government, which has poured more than $3 billion in direct aid into the railroad since its beginning on April Fool's Day, 1976. But if the Reagan administration's budget director, David A. Stockman, gets his way, Conrail is about to go off the federal dole.

Stockman and others among the Republican newcomers at the Office of Management and Budget are not much for billion-dollar subsidies to losing propositions. They have announced that the administration "intends to wean Conrail from all its federal subsidies." The budget that President Reagan sent Congress last week calls for a $300 million appropriation to get the railroad through the rest of this fiscal year and all of fiscal year of 1982. Beyond that, the budget calls for no more federal subsidies to Conrail.

Conrail is on the Reagan-Stockman "hit list." But the "weaning" that OMB has in mind for the railroad will be far more difficult than erasing a few lines of appropriations from the federal budget books that went to Capitol Hill last week. Conrail was created because it provides a vital service to thousands of communities. Even ardent budget-cutters in Congress may question the administration proposal if communities in their districts are threatened by the loss of rail freight service.

At the very least, however, OMB appears to be proposing an end to the Conrail subsidy at the right time. Long before the Republican budget-cutters arrived, general agreement was emerging that the status quo is not acceptable, that the government should not simply continue to feed Conrail's deficit. But beyond that there is no consensus about Conrail's future or the advisibility of the administration's plan to cut off all government funds after 1982.

The general dissatisfaction with the current state of Conrail was evident when Congress enacted legislation deregulating the railroad industry last year. As part of that legislation, Congress ordered studies of Conrail's future by the railroad itself, by the Department of Transportation and by the U.S. Railway Association (USRA), which was established by Congress to monitor Conrail's performance.

USRA has already produced one report, and along with the other agencies is due to have a final report and recommendations for Congress by the end of this month. The first report, issued last December, established a clearly critical tone regarding Conrail's future as a dependent of the federal government.