Well I somehow posted this in the wrong place, and now can't delete or edit it.

I think the parents mistook the sister's rare flower ability for the Saint that's supposed to appear once in a generation. They mentioned at some point that there is supposed to be one. Between that, and the brain drain mentioned towards the end of the story, my theory is that all the ice mages, together, passively maintain the palace. Because of the parents' short-sighted policies, they began actively driving ice mages out of their kingdom, leaving more and more of the work for MC's passive ability to handle. Once that literal Saint was gone, there just was no longer enough ice magic to maintain their home.