On a current playthrough, first time encountering this problem. Both of my sims are 4 star celebrities. One of my sims has continued to accumulate points, while the other did not accumulate the points of her third star, I got her to 4 stars without any cheats and she did gain her fame points but not the back due points. I have repaired my game files. I have not used and cheats. No mods or cc installed.
Probably not it, but did you spend the fame points to buy perks for that sim and not for the other one? And do you have access and are able to select any of the 4-star level perks? If the sim is gaining points now, then that's the only thing I can think of for the sim not to have any points.
One thing you can try to see if you can get the sim gaining fame points is to quit the spotlight, then reenter it. The sim will lose all their points and perks, but fame should start to build again by doing options that gain fame and the sim should gain them back.
Hope this helps.
