The Professional Air Traffic Controllers Organization has lost the first round in its battle to save its status as bargaining agent for 12,000 fired controllers and to force the Reagan administration to return to the bargaining table.

PATCO is still the bargaining agent for the controllers although most of its members have been out of work since early August when they were fired for failing to show up for work. PATCO had gone to the Federal Labor Relations Authority -- it handles in-house labor disputes -- alleging that the Federal Aviation Administration had committed unfair labor practices by failing to bargain seriously with the union, forcing its members to go out on strike. The FLRA also is considering a government motion that PATCO be stripped of its right to represent controllers because it led them out in violation of the federal no-strike law.

In the case of PATCO's allegation that the government was guilty of unfair labor practices, FLRA General Counsel H. Stephen Gordon ruled against the union this week. Gordon said an investigation by his office indicated that PATCO, on July 31, went before TV cameras and reporters and threatened to strike on Aug. 3 unless negotations were completed.

The union was asking FAA endorsement of legislation that would have given controllers immediate five-figure raises and a shorter work-week. FAA had a very different package in mind, and warned that anyone striking would be fired. Under federal law, employes who strike Uncle Sam can be fired, fined up to $1,000 and jailed for a year and a day, or all three.

The FLRA next week is due to rule on the government's request that PATCO be decertified as bargaining agent for controllers. Whichever side loses is expected to take the case to the U.S. Court of Appeals here. If PATCO is decertified, other organizations or unions could move in and begin organizing controllers, and presumably resume contract talks with the FAA. If PATCO is allowed to remain as the bargaining agent, FAA could be forced to deal with it, particularly if it represented controllers who are still on the job.