I don't wear power armour, but I've got three different sets of T-45 power armour that I've painted, all sitting in Sanctuary. None contain fusion cores.

Problem is that after coming back from a brief excursion not only are they not painted any more, but they are missing bits, such as the helmet, left arm, or right leg.

I'm afraid to rebuild them, because if this happens too many times, I won't have any components left.

Have you checked everybody's inventories? I don't know how but it somehow seems more likely that they've relocated than straight up vanished.