THEATRICAL institutions, like government programs, occasionally arrive at a time in their lives when no one can quite say why they exist. The vital signs are still present. They go on producing plays and soliciting grants and disbursing paychecks and holding opening-night parties, but with an air of duty rather than pleasure. The ability to survive has outlived the ability to inspire, and the public -- or the portion of the public that keeps coming -- gradually stops expecting to be excited and starts taking slapdash and humdrum efforts in stride.

Theater in Washington is the product of how, each year, a number of institutions decide to allocate their resources (in contrast to New York, where more of the key decisions -- to launch or not to launch -- are made by individual entrepreneurs). So when an institution loses track of its reason for being, or fails to find one, the Washington theatergoer is likely to feel it where it hurts.

This is what seems to have happened, in varying degrees, to two local theaters founded a decade ago with much hard work and high purpose. Both are run by nonprofit institutions, and both face a constant struggle to raise money for projects that might never stand a chance in the commercial marketplace. But their problems demonstrate, I think, that the commercial marketplace has no monopoly on lack of artistic integrity and direction.

Ford's Theatre does a consistently impressive job of reminding the public about the time and energy that went into restoring a landmark building and permitting live performances there. The management has succeeded in spreading an aura of civic and social importance over its productions, and in securing the attendance of presidents and other prominent folk. But the attention that has gone into image maintenance has rarely been matched by the attention that has gone into the shows themselves. Amateurism and professionalism have become so thoroughly confused, in fact, that even performers of proven ability -- witness John Cullum in the recent "A Christmas Carol" -- seem to have asked little of themselves on the Ford's stage.

Kennedy Center chairman Roger L. Stevens says he has never been happy with the status of the Eisehower Theater as a "booking house," taking in whatever touring shows his producer colleagues have chosen to offer. In his own capacity as a producer, Stevens has given the Eisenhower a measure of identity by sponsoring the works of Preston Jones, Arthur Kopit, Tom Stoppard, Harold Pinter, Alan Ayckbourn and others, but over the last two years the Center's efforts to get beyond the usual pre- and post-Broadway product have led to some of its flimsiest and least popular offerings -- "Daisy Mayme" (a Jean Stapleton vehicle mounted by Pennsylvania's Totem Pole Playhouse), "Home and Beauty" (a Rosemary Harris vehicle produced by the Center for -- it turned out -- local consumption only), "Richard III" (a Michael Moriarty vehicle that played both here and at the American Shakespeare Festival in Stratford, Conn.), and now "A Partridge in a Pear Tree" (the first venture of Empress Productions, a new group intended to have an ongoing relationship with the Center).

The Ford's and Eisenhower predicaments have a broad historical pattern in common. Both organizations have toyed with the idea of an ongoing theater company, and both have been through short-lived (or stillborn) alliances with people who have run such companies -- in Ford's case, Michael Dewell and Ted Mann (during the first few years after the theater's 1968 reopening); in the Eisenhower's case, Richmond Crinkley (during the Bicentennial season) and Joseph Papp (in 1979-80).

Except for those brief flirtations, however, both theaters have been dominated by strong executives, Frankie Hewett and Roger L. Stevens, who came originally from non-theater backgrounds and have had to juggle bureaucratic, business and artistic decisions simultaneously -- multiple demands that may help explain why both have been making more last-minute booking decisions lately and looking to more obscure and less proven sources of supply.

And the unfortunate bottom line of the comparison is that at both theaters, even minimal standards of professionalism and competence have been strained by some recent productions.

Inevitably, such parallels are unjust to the particulars of each case. Many important plays have occupied the Eisenhower Theater during its first decade, and the creation of the Kennedy Center is an achievement of unique proportions for which Stevens has won justified acclaim. Hewett and the Ford's Theatre Society, on the other hand, have had to deal with an unusual auditorium, minimal backstage facilities and tight restrictions imposed by the National Park Service. Another notable difference is that Stevens had spent two decades as a producer before the Eisenhower Theater opened its doors, while Hewett was a fund-raiser and lobbyist before taking over the Ford's operation in 1971.

As 1981 gets going, the Kennedy Center is once again alive with plans to launch its own theater company -- commencing, it is hoped, next fall. (In a parallel move where musicals are concerned, Stevens has helped form the American Musical Theater Group, a national producing consortium of art centers.) So the Kennedy Center is aware of its identity problem. The question is whether the problem will be addressed boldly or half-heartedly, whether the Center's management will delegate sufficient resources and authority to people of sufficient standing and clout. Up to now, the Center's operations have been marked by a consistent lack of enthusiasm for such delegation and such people. And while no venture can be prejudged on the sketchy announcements that have emerged so far, Stevens' avowed distaste for naming "some hot-shot director" to run the new company is discouraging. In the theater's unending struggle to attract first-rate actors and authors, a prestigious artistic director (or perhaps a directorate on the current model of Lincoln Center's Vivian Beaumont Theater) can be very effective bait.

It is no coincidence that most of the best acting on the Eisenhower Theater stage has been done by stars of (shall we say) mature vintage -- Henry Fonda, Geraldine Page, Jason Robards, Julie Harris, Hume Cronyn, Jessica Tandy and the like -- while we have seen relatively little of the generation exemplified by Robert Duvall, Blythe Danner, Meryl Streep and Al Pacino. Such people are willing and, sometimes anxious to work in the theater, despite the greater income to be had elsewhere. But the directors, producers and playwrights likely to fire their enthusiasm are ones who have not, by and large, been pursued by the Kennedy Center.

This is partly a question of old friendships and loyalties and partly one of taste. While no one can pigeonhole the style of an institution that has presented such diverse (and laudible) productions as "Wings," "The Royal Family," "A Texas Trilogy" and "On Golden Pond," Stevens has shown certain clear preferences -- for the Kin's English over the streetwalker's, for personal themes over social and economic ones, and for clashes of words rather than blows. These preferences -- and the consequent failure to present works by such coming American playwrights as Michael Weller and David Rabe -- may be due for a fresh cost-benefit analysis.

Ford's Theatre has come close, I think, to carving out a sensible and distinct identity for itself as a home of "family entertainment." The phrase may be distasteful, but the concept -- as expressed by such popular choices as "Mark Twain Tonight," "Your Arms Too Short to Box With God" and James Whitmore's one-man shows -- fits a theater of bright colors which happens also to be a child-oriented museum. Ford's failure has been a nuts-and-bolts one, and the solution must involve a campaign to bring them the tools they need, and hold them accountable for the result.

For all their problems, the Eisenhower and Ford's enjoy enviable national reputations among artists as well as audiences -- partly because of geography and sentiment, and partly because of the labors and achievements of the present managements. The trouble is that, of late, these reputations have been spent faster than they have been replenished -- a pattern that doesn't work any better with a reputation than with a bank account.