Wizmode testing says no. If you kill the royal jelly while worshiping Jiyva (which is somewhat frustrating to do and places you under immediate penance for attacking it. Oddly however, the summoned slimes created while under penance were neutral) and then abandon him, the altars stay, and you can rejoin.
If we wanna justify this from a Small Gods perspective- I got some 'splaining.
Having believed in Him is different from never believing at all. So it's not that Jiyva now has no believers- he has no believers who
worship him. Who pay him respect. As long as you're alive, there's still one mortal who accepts his existence, even if you regard him with distaste or hatred now. You would have to master double-think or die to remove the last vestiges of belief.
Edit: dang ninjas!
Double Edit:
MarvinPA wrote:Jiyva is angry enough at you to stick around and give penance, before ceasing to exist once it's done.
Went back to wizmode and confirmed. If you mash 5 long enough, eventually the little jello altar stops dancing and vanishes. Jiyva is powered by hatred.