AS THE Rep Inc. winds up its 10th anniversary season, executive director Lyn Dyson has no hesitation about naming its biggest achievement: survival.

"It's a miracle the doors are still open," he says. "Everywhere you hear theaters saying, 'Without more money, we'll go under.' We'd be saying it every day, too, if we didn't go out and cut deals with people to keep the phone and electricity on and the rent reasonably up to date."

Part of the problem, Dyson believes, is that the Rep has been saddled with a misleading image. The theater was founded in 1971 by actor Robert Hooks, as the D.C. Black Repertory Company. An Equity operation, generously funded by the Ford Foundation and launched on waves of publicity, it was expected to do for Washington what the Negro Ensemble Company does for New York. The black middle class never turned out in significant numbers, however, and five years later the theater was on financial shoals.

Hooks and some of the company members called it quits. Others, however, decided to stay on. Cutting back on the budget and even the name, they reorganized as the Rep, a non-Equity company, and moved into new quarters at 3710 Georgia Ave. NW. It has been touch and go ever since.

"Even though the Rep was there to carry on, a lot of people didn't know it," says Dyson. "I think we had to go through a period of four or five years for the public to forget about the failure of the D.C. Black Rep and allow us to move forward on our own merits. But that's happening now."

At 29, Dyson is a determined optimist, which allows him to overlook those occasional ends-of-the-month, when members of the Rep's small staff (artistic director Jaye Stewart; managing director Carolyn Smith; director of the children's theater Sadiqa Pettaway) are obliged to forgo their paychecks. He prefers instead to point out that Mayor Barry recently designated the Rep as a major cultural institution in D.C. and recommended it for a $45,000 grant next year. (The D.C. City Council, however, promptly responded that it wasn't the mayor's job to earmark funds for specific arts groups and turned the decision over to the D.C. Commission on the Arts, which has yet to announce its grants.) Dyson says he's struck a deal with Howard University's television station, WHMM, which would allow the Rep to move into cable television. He's also hitting up local businesses for support and finds them receptive, even if no purse strings have yet been loosened. (The Rep's annual budget hovers around $125,000; Dyson would like to see it go to $300,000.)

Even Reaganomics, which has most theater directors howling like pinched curs, doesn't faze him. "Reagan may be the best thing that's happened to black people," he says. "It's caused us to come together, to push harder for visibility, to go after the private sector. I've always believed in self-help programs. I can see us producing plays on Broadway. Touring the Caribbean and Europe. If you don't have that vision, you can get caught up in the moment. And the moment can be disastrous."

Dyson admits that some of the early fare--the "get whitey" plays, or the back-to-Africa rituals--may have alienated more spectators than they attracted. "Maybe the D.C. Black Rep should have opened with something like 'Porgy and Bess,' the tried and the true. But that can be debated forever." With last fall's "A Kiss Too Late" or the current "Eden," he believes the Rep has shifted to plays that "celebrate the unity of the black family."

Much of Dyson's faith in the Rep, as a training ground for black actors, is rooted in the fact that he himself rose through its ranks. Rejected in 1971 "like everyone else" in his bid to be part of the company, he tried again in 1973, was accepted into a tuition-free workshop and subsequently played leads in such shows as "Don't Leave Go My Hand" and "Among All This You Stand Like a Fine Brownstone."

"The potential of this place is enormous," he says now. "Sure, there are moments when all of us throw our hands up in despair. Mine are very brief."