Tossing in spoiler tag as a precaution.
So at the end of Season 1, RF's direct linear ancestor kills himself thus erasing RF. However the result was a time storm/singularity event. I still say this was caused by the erasure of RF and not a trap he left behind for them to deal with as he went home to the future as that would risk his future and his life.
Also reference the Season 2 finale of Beast Wars for a similar time storm/singularity event.
Then we had a time remnant of RF from before his erasure running around in Season 2 and for a Season in Legends before Black Flash finally caught up with him.
However Rip Hunter has formed a new time organization to deal with aberrations in the time stream. One would think that the erasing of RF and the time storm/singularity would amount to a rather HUGE aberration.
An aberration that can only be fixed by preventing Eddie from killing himself and for Rip Hunter to send RF back to his own timeline.
Thus RF lives and we get 2 seasons at least of revisions to the Flash tv series and a season revision of Legends from the time changes. Thus the poor version of Flashpoint is undone, Caitlyn may not become KF among other things.
Or the simpler methods would be:
1. An RF from an alternate Earth arrives to menace Barry. a simple solution which I think is happening in this season's crossover event.
2. Someone else takes up the name of the Reverse Flash.
Berlanti has said in interviews that he doesn't care if the internal logic of the show makes no sense, and at this point I've suffered through enough bad science, impossible paradoxes and awful, nonsensical plotting that I've just thrown in the towel and resigned myself to sitting back, gritting my teeth through the bad bits, and enjoying the show for what it is.
Saying that, I'd prefer to never, ever, ever, ever, EVER see another time travel story on The Flash as long as the series lasts. Ever. So if they do bring Reverse Flash back on a semi-regular basis, I'd prefer that it's a parallel world version of him. That way we avoid unworkable explanations for how he survived, we avoid another unworkable time travel story, and we avoid unworkable paradox every time he appears.
So, a PW RF for me, please!