The Metro Board, which decided some years ago to impose automatic fare collecting upon the Washington subway rider, is beginning to lose patience with the $53 million Farecard system its decision bought.

Metro Board chairman Jerry A. Moore Jr. discovered for himself yesterday what every regular Metro rider already knew: that Farecard vending machines frequently are out of order, that entrance and exit gates stick and that long lines of increasingly surly patrons are lining up at the swamped fare machines that are not out of order.

"I do not know the answer to the $50 million disaster we have out there, but we must find the answer," Moore told his board members at their regular weekly meeting yesterday.

"In my mind, these machines have to go," Prince George's County board member Francis B. Francois said. That was the first outright call for the dissolution of the Farecard system by a board member since the system was introduced two years ago.

Metro General Manager Richard S. Page, who once said almost the same thing when he occupied a high federal office before taking the Metro job, promised the board members he would submit proposals to them within a month.

"Basically, there are three alternatives," Page said. "We can make the present system work better; we can change our fare structure so we could abandon parts of the present Farecard system, such as the exit gates and the addfare machines, or we can abandon it altogether."

Page said he is planning a meeting with top executives of Cubic Western Data, the San Diego-based manufacturer of the Farecard equipment.

Cleatus Barnett Montgomery County board member, said that "Cubic owes Metro its entire resources to make this work." If Cubic is unwilling to make that commitment, Barnett said, he would join Francois.

Farecard was born during Metro's planning days from a decision by board members that subway riders traveled: the longer the ride, the higher the cost. This was to deal with the old argument in transit that a flat-fare system penalizes close-in city residents and subsidizes long-haul commuters. The only way to compute the fare based on mileage was to force the rider and his ticket through both an entrance gate and exit gate. Electronic gadgets would compute the fare and deduct it from the ticket.

When the complexities of the electronic fare collecting on the subway were combined with the already Byzantine bus fare schedule, Metro retired the trophy for most complicated fare schedule in the United States.

Page also told the board yesterday that Metro has overcome another crisis in the availability of subway cars for daily service with the arrival of critical parts.

However, Page said, even with all the cars it owns operating properly, Metro will not have enough cars to open the Red Line extension from Dupont Circle to Van Ness Center, now scheduled for the fall of 1981. There will be enough cars, but they will be crowded, he said, for extensions of the Orange Line from Rosslyn to Balston and of the Blue Line from Stadium-Armory to Addison Road.

Metro recently authorized the purchase of about 90 new subway cars, which should begin arriving in the summer of 1981. It is possible, barring the usual delays in subway car construction and delivery, that the cars will keep pace with the construction schedule.