The hope that television will someday produce a richly textured, uncliche'd, genuinely moving account of a noble chapter in American history is raised again, and dashed again, by "For Us, the Living" (9 tonight on Channels 26 and 32).

This 90-minute docudrama comes on the 20th anniversary of the murder of Medgar Evers, who led the campaign to break segregation's hold on Jackson, Miss., and stuck to it even when he had every reason to think he was about to lose his life.

It's hard not to admire any effort to honor Evers, but it's also hard to avoid the conclusion that television knows only one way to approach this type of subject matter: laboriously.

There are affecting moments--especially in the early going, when the ordinary black citizens of Jackson become infused with Evers' enthusiasm for nonviolent resistance, and at the end, when Evers lies dying, surrounded by his wife and family (who aren't permitted to go to the hospital with him because it's a white hospital).

The most affecting moment of all, perhaps, is the very last, when, over a shot of Evers' tombstone, the voice of his widow comments: "Somewhere in Mississippi lives the man who murdered my husband. I wonder what he thinks of Jackson with its now-integrated department stores and libraries and schools . . . It's better, Medgar, it really is better. But please know, my dearest, the struggle goes on."

And yet when we overhear the actors in the TV version of the Evers family in conversation, they don't seem to be talking to each other but to posterity. "You've got to realize that what you're doing is right and that I support you all the way," says Evers' wife at one critical stage of the struggle. "It's going to get better, Medgar, it has to."

On the night of his death, Evers tells his young son: "No matter what happens when I'm away, you remember that you're the man in this family." To his wife, he adds: "Remember, honey, be strong."

"For Us, the Living," part of PBS' "American Playhouse" series was based on the memoirs of Evers' widow, Myrlie, now director of consumer affairs for the Atlantic Richfield Company. Many able people have contributed to the program, including playwright Ossie Davis, author of "Purlie Victorious," and director Michael Schulz, who made the films "Car Wash" and "Cooley High." The cast, featuring Roscoe Lee Browne and Paul Winfield in addition to Howard Rollins Jr., whose portrayal of Coalhouse Walker in "Ragtime" got him nominated for an Academy Award, could hardly be improved on.

But as the story builds to its climax, we see the same old bands of malevolent rednecks prowling through the southern night, tossing Molotov cocktails to the accompaniment of the same old melodramatic music, and all that talent seems to have gone for naught. It seems that there is an inviolable process at work here before which individual writers, directors, producers and actors--not to mention audiences--stand helpless.