Auto-Train Corp. yesterday revealed it lost $663,000 in the first quarter of 1979 and belatedly issued its 1978 annual report showing a $4.4 million loss for the year.

The first quarter loss contrasted with a $685,000 profit in the same three months a year ago and was the worst first quarter ever. The company traditionally earns most of its profitsduring January, February and March, when travel is heavy to Florida.

In heavy trading on the American Stock Exchange, Auto-Train shares closedyesterday at 5 3/4, down 1/2. The stock was the week's most active issue on the Amex. All told, 958,900 shares changed hands, equivalent to 60 percent of the company.

The stock was up 50 cents for the week, but went down for four days in a row after closing Monday at 7 3/4. Auto-Train shares took off from a record low of less than$2 a share two weeks ago on the strength of speculation the company might benefit from report of gasoline shortages.

During the flurry of activity investors had no access to current financial data about the company, because Auto-Train's 1978 annual report was not filed by the deadline required by the Securities and Exchange Commission.

SEC attorney Jonathon Eisenberg, who has headed a prolonged investigation of Auto-Train, said he could not comment on any action that might be pending over the violation of the filing deadline.

The annual report filed yesterday revealed Auto-Train's auditors, Alexander Grant & Co., are concerned about the continuing financial viability of the company.

"A major portion of the assets" of the company, the auditors warned, is "dependent upon the company's ability to meet its financing requirements, to maintain present financing and the success of its future operations."

Auto-Train's "financing requirements," the report shows, include borrowing $6 million- $3 million from an insurance company and another $3 million guaranteed by the Economic Development Authority of the Department of Commerce.

The company has defaulted on some provisions of a loan agreement with major lenders have waived the requirements and given AutoTrain more time to pay. The Seaboard Coast Line railroad has also given the company additional time to pay its bills for use of Seaboard's tracks and crews to run the Auto-Train to Florida.

Auto-Trains's financial condition was so perilious last November that President Eugene Kerik Garfield had to put up $100,00/ of his personal funds to guarantee a loan for the company. The loan has now been repaid.

The report also discloses that nearly a quarter of Auto-Trainhs 215 pieces of rolling stock is out of service. About 25 cars have to be refurbished before they can be used and seven have not been repaired since they derailed in February, 1978.

Auto-Train's revenues for 1978 amounted to $27.9 million, compared with $29.8 million in calendar 1977. The $4.4 million loss-equivalent to $2.69 per share-contrasted with a $520,000 loss (32 cents) in 1977.

The company's first quarter report to the SEC, which was due last week, will be filed on Monday, a spokesman said. Yesterday's announcement said the 40 cents per share loss-contrasted with a 42 cent profit a year earlier-was due to increased competition from airlines, severe winter weather, and "restricted capacity."