A group of Washington investors hopes to bring back the Auto-Train next fall, but first they must enlist the aid of two institutions that have steadfastly refused to help save the bankrupt railroad.

Washington attorney G. James Frick said the end of Auto-Train service last Friday won't stop efforts of a group he represents to reorganize the company and bring it out of bankruptcy.

Frick's group includes half a dozen Washington investors and business people. The most prominent of them is J. William Middendorf, chairman of the board of Financial General Bankshares Inc. and the Reagan administration's choice to be ambassador to the Organization of American States.

Middendorf told a reporter at Financial General's annual stockholders meeting in Richmond last week that he has not been actively involved in the Auto-Train rescue recently.

Frick said the investors have reached agreements with all of Auto-Train's major creditors except for the Seaboard Coast Line and Richmond, Fredericksburg and Potomac railroads. The two railroads provide tracks and crews for Auto-Train's route from suburban Lorton to Florida.

The investors also plan to seek help from the Federal Railroad Administration, he said. The FRA has legal authority to give government-guaranteed loans to struggling railroads but has refused to aid Auto-Train in the past.

Seaboard not only urged the FRA to turn down the request for a federal bailout but also made repeated efforts in federal bankruptcy court to shut down Auto-Train.

The two railroads have told Frick's group they will not let them use their tracks unless the investors personally guarantee $2.5 million of Auto-Train's debts to them.

Seaboard and RF&P are believed to be the biggest losers in the Auto-Train bankruptcy, although a complete listing of the railroad's debts has not been made public.

The railroads, which charge Auto-Train $23,000 a day for their services, have earned millions of dollars from Auto-Train over the last 10 years.

But executives of the two railraods have been embarrassed by losing several million dollars in the bankruptcy.

Not only does Auto-Train owe the railroads millions of dollars for services, but also the two roads were forced to pay off $2.6 million of Auto-Train's other debts. They cosigned an Auto-Train bank loan. When the loan was not paid, Seaboard had to put up $2 million and RF&P $600,000. Marriott Corp., which provided food on Auto-Train, guaranteed $400,000 of the company's borrowings and lost that money along with what the company lost on unpaid food bills.

The two railroads were so anxious to be rid of Auto-Train that they agreed to put up $800,000 each to pay for Auto-Train's final week of operations and to finance expenses involved in shutting down the company entirely.

In return for the $1.6 million, Auto-Train bankruptcy trustee Murray Drabkin agreed not only to stop the train but also to cancel the long-term contract with the railroads, freeing them from future obligations.

Frick said his group is counting on negotiating a new contract with the railroads that will permit resumption of Auto-Train service this fall.

The group invested $400,000 in Auto-Train last December and stands to lose that money unless it can revive the route. Frick earlier told a federal bankruptcy court that the investors hoped to make a proposal by May 1. Last week he said the plan will be presented later.

Auto-Train has never made money during summer, when travel to Florida is light. Frick said it may be possible to run a seasonal service and close down during hot weather.

Because bankruptcy proceedings will wipe out Auto-Train's old debts, it should be possible to resume operation with about $5 million in capital, Frick added. The group also hopes to get a $2 million to $3 million government-guaranteed loan from the FRA. When the FRA turned down a similar Auto-Train request last year, however, it described the route as not an essential public service and said it did not appear capable of operating successfully even with government help.

Whether the Reagan administration will reverse the Carter administration officials remains to be seen. Budget director David Stockman has pledged to slash government-guaranteed loans. Secretary of Transportation Drew Lewis says he wants to end federal subsidies to Conrail, the northeast corridor rail line, and slash government support for Amtrak, the national passenger train network.

In light of those policies, aid to Auto-Train may be unlikely. It will be a politically touchy decision for the administration. Middendorf is a prominent Republican, and another member of the group is Carl Shipley, former District of Columbia GOP chairman.

Direct government intervention might save the service by making it a part of Amtrak. Bankruptcy trustee Drabkin said he approached Amtrak about a takeover last year but was turned down by Amtrak President Alan Boyd.

He said Boyd was anticipating cuts in his own budget and did not have funds needed to rehabilitate Auto-Train's passenger cars. The cars were taken out of mothballs and rebuilt when Auto-Train started 10 years ago and now require another overhaul.

Amtrak already runs trains over the Auto-Train route and could run its own Auto-Train service for much less than it would cost an independent railroad.

Amtrak may be the only answer, because of the reluctance of Seaboard and RF&P to help save the train.

"Let's face it, they've been burned," offered John (Tom) Tucker, Auto-Train's long-suffering public relations consultant. "They don't want anything to do with this railroad, and who can blame them?"