If they've got a human vessel, that in itself can be a hard limit! There's only so much a humanoid body can take. Especially so if they value this body out of sentiment and want to preserve it. This feels video-game-y but if you want to simplify it, you could apply the "I can only expel this amount of energy after eating this amount of food or else I'll pass out" kind of thing. A more desperate version can be like "I need to eat because I haven't done so in 3 days and I'm literally about to die" and etc. etc.
Another possible limit for a deity can involve the strength of faith. Do a lot of people still believe in them? Do a lot of people forsake them? Maybe that can tie to how well they can use their powers. They can be weakened due to low morale, they can lose control due to unstable emotions, etc. You mentioned that the goddex gets stressed so there's that too.