Will a villager's eligibility to be chief ever change? I.e., If I look for a new chief, have a villager try the robe and it doesn't fit, find a chief, have the new chief die, then is it worth trying the same other villager later or will the robe always never fit?

Yes, I believe so. It happened to me when I had a wave of Elder chiefs.

I think when a chief dies the game picks another villager randomly. So, yes, just because it didn't fit before doesn't mean it won't fit later.

Thanks for the info, folks.