My sim keeps losing her Celebrity stars?-issued fixed-

If you want to disable celebrity depreciation entirely, just set all the levels to 0. Then you might actually see some other celebrities around. They're probably losing their points too fast to get any stars. In my current game, I have depreciation disabled, because my sims live in a rural, small town world, like I do in real life, and where I live, everybody knows everybody else's business, and it's pretty much once a celebrity, always a celebrity.