Ahsoka survives the entire original trilogy: she appears in the very last scene on Rebels which is set after ROTJ. After that, there's no official word unless it's been mentioned in a novel or something.
As to why she doesn't appear in the trilogy itself, that's easily explained because the focus is on Luke Skywalker and his group. In the first film, the only members of the Rebellion you see are the ones on Leia's ship at the start, and then at the base at the end, and the latter for only a few hours of in-universe time. Ahsoka could easily have been somewhere else during that brief period.
In TESB she could have been on Hoth and evacuated with the others near the start, and you don't see any other rebels aside from the main characters for the rest of the film.
In ROTJ, again the first part of the film is focused on the crew on Tatooine, so no reason for Ahsoka to be there. The only times she'd have a legit reason to appear would be the Mon Mothma/Ackbar briefing prior to the mission; otherwise the rest of the film--not counting the ending scenes--is focused on the strike team on the moon, on Luke on the Death Star, on Lando (and Wedge for a few seconds), or on Ackbar on his command bridge. Ahsoka could have literally been anywhere during that battle and she never would have appeared.
And that's assuming she was there at all and not doing all sorts of other Rebel-like things somewhere else. In ROTJ, for instance, aside from the small infiltration team, it was the Rebellion naval force that was being used at Endor. Any ground forces they might have would have had no reason to be there, and she could have been off with them as, despite certainly being able to fly, she's been primarily portrayed as a ground combatant.
