Why was that third stooge slot always rotating ...

Perhaps it was one of those weird Hollywood jinx things.

Shemp was the original member of the Stooges during their early years... Moe, Shemp and curly were actual brothers. Curly then stepped in and after his stint he was replaced again with brother Shemp after Curly suffered a stroke.
Shemp had a brief return then suffered a massive heart attack and died.
Moe and Larry Fine looked for replacement members after that.