The pieces may be coming together by accident or design -- for a breakthrough in the year's longest-running strike, the air traffic controller walkout that has cost 11,000 feds their jobs, caused delays and layoffs in the airline industry and given organized labor a badly needed anti-Reagan rallying point.

Unions, particularly the Professional Air Traffic Controllers Organization, believe the strike is still winnable. They think (hope) most controllers will be rehired either through court action or because public pressure -- over airline delays and the safety issue -- will force the government to back down.

Despite the no-rehire policy, the Federal Aviation Administration has quietly taken back 56 controllers who said they made a mistake. That return route, however narrow, is open.

Politicians -- between voters who think PATCO got what it deserved and those who lost jobs or feel PATCO is the victim of union-busting -- would like a diplomatic solution to the problem without making either the union or the government eat crow in public. Consider what is happening:

* The Federal Labor Relations Authority has been a long, long time deciding whether to decertify PATCO as the controllers' bargaining agent. Some people find that significant. Others think FLRA is simply trying to build a solid case that will withstand the appeal that the losing side -- either government or PATCO -- will certainly make. (Newsday has reported that the FLRA already has decided to decertify PATCO, but FLRA refuses comment.)

* The House Post Office-Civil Service Committee says the 10,000 people manning FAA's "patchwork" system (nonstrikers, supervisors, reemployed retirees and loaned military personnel) are working harder, longer and using less sick leave than the controllers they replaced. But the report prepared by the Democratic staff of the committee says the system faces "serious" problems by late 1983 because FAA cannot train enough competent controllers fast enough to bring the system back to normal. Without mentioning PATCO once, the committee report concludes that experienced controllers must be found -- fast -- to avert trouble.

* Congressional leaders are urging FAA to ease up. Chairman William Ford (D-Mich.) of the PO-CS Committee and others question whether the government can legally or morally close employment for life to persons who have struck it.

"I don't believe in a grand design for the universe or for this situation," a PATCO official said yesterday, adding that "the only thing that is clear is that the government wants PATCO's hide."

An FAA official said, "I just don't see how this administration can take them (the controllers) back. Hell, Meese (Edwin Meese, considered President Reagan's closest aide) has said several times the strikers won't be rehired and he is closer to Reagan than anybody but Nancy."

Some observers believe that more controllers will be taken back if they say they were intimidated into striking. (One person was rehired, FAA said, after she brought an affidavit from her minister testifying that she had been frightened by pickets and came to the minister for advice).

Both sides are in their tough, public crouch: PATCO and other unions insist government wanted the strike and drove PATCO to it, but will lose anyhow. The administration says the controllers are lawbreakers who had their chance to come back.

Both sides are quietly wondering who will get the blame for the next major airline disaster when it happens. Those of us in the middle, who fly or whose loved ones do, wish the airborne game of chicken (played with real people) would end before something more precious than the egos of politicians -- union and government -- gets hurt.