Sorry, this response is coming quite late.
I don't think they should respawn, because that would lead to easy iron-farming which is bad. To prevent the death of the golem (or golems, if a village spawns with multiple "golem huts" (which shouldn't be too likely)), I would have the AI stay to village paths, only straying from them when a zombie is within attacking range (which only triggers when it's possible to walk there, I believe). It wouldn't stray more than some specified distance from the village, and it would then walk the same blocks on its return to the village. During the day it would stick to the hut and regen its health. If a golem was built inside this house instead of just anywhere, it'd be one of these golems tied to the village, which the game already has code to support since player-made golems are actually different from naturally spawning ones.