Coved shower ceiling, no fan, cracking paint

Hi all, I'm new here, so please feel free to redirect me to a different forum if it's more appropriate. We currently are renters in a 1927 apartment building (remodeled in '09). Our shower has a coved ceiling with a lip that drops down ~15" along the outer edge, creating a nice little pocket for moist air. There's no exhaust fan, so we just leave the window open at all times and hope for the best. Unfortunately the ceiling paint is now cracking/flaking pretty significantly. Certain parts of the ceiling (plaster w/metal mesh backing, I believe) are also slightly soft to the touch, at least when I'm in the shower. Is this an issue that we/a handyman can remedy with a better sealing paint? Or is it a bigger issue for the landlord to address long-term? Thanks!