It wasn't designed to serve as a museum piece for decades on end and is now falling apart under its own weight. It not only needs to be repainted but rebuilt as well with structures that can better hold it together for an extended period of time.
This is certainly true, but leads back to the already-invoked "Ship of Theseus" issue.
It depends on how seriously you regard the model as an historic artifact. If it really, really is important that it be preserved at all costs, then the preferable answer is that it be taken off display and stored in some fashion that preserves it and protects it from further damage, with all of its (remaining) original interior construction and wiring intact. A more durable replica, built by direct reference to and perhaps molds taken from the exterior parts, could be constructed for public display.
This is done with all kinds of museum artifacts that are considered irreplaceable and that can't be safely displayed.
Any solution, of course, involves a lot of money. Paramount offered to get involved in the NASM 25th Star Trek exhibit with the kind of cash a studio could bring to it, but there had been a couple of public kerfluffles regarding corporate sponsorship and its influence on the content of exhibits at that time (reportedly
, among other things Paramount would have wanted a presentation that emphasizied their then-current Trek products to a greater degree).