They will respawn forever, if there is some open land for the program to stick them back into.
I chased the Japanese and the Americans all the across the expanses of a V shaped continent. The Japanese respawned 4 times and then respawned onto an island where I left them. The Americans respawned 4 times as well with the last respawn truning them into boat people that never could land. They only had a Galley with a settler and a spear inside. No capital city; no City at all in fact. Just a leader who kept wanting to trade a territory map for techs. (yeah, what territory abo ole buddy).
The respawning thing is buggy and one of the biggest examples of flawed logic in the Firaxis releases of late.
Turn it off permanently. Hopefully Firaxis will make that the default setting in the next release, before more people get frustrated.
If you want more civ opponents, up the count in the editor. If you want more combatant opponents up the barbs level. Watch out for barbs though, because that software is buggy as well and an idiot programming mistake has the barb villages programmed to go mental all in the same turn, of higher barb levels with explorer games and lots of open space, the barb bug mean that you can get 30 or 40 raging horsemen screaming out of the boonies from different directions all in one turn.
Good luck