If the paint is easily peeling off the caulk- ( soaking in is kinda throwing me..) I am suspicious that someone used the dreaded silicone caulk.
Does paint-water, anything bead up on the caulk? If so - that is the problem.
And a cursed problem it is- hard to fix- so one again I
will say to whoever listens-
DON"T USE !100% UNPAINTABLE Silicone caulk unless you really know why you are doing it and what that means!!
Meanwhile- check it out and see if that looks like the problem.. I'll hold more rant till later..