Thanks @Sid1701D9 I didn't realize there were different colors on that bar. You can never lose more than two levels of fame, according to the lesson on the Fame System (Options Menu/Lessons/Get Famous/Fame System), so you're probably right that the darker green is locked.
Be sure to use your perks. The PR Agency can boost fame with either a Good Story or a Bad Story, even if there's no one around. Getting invited to another celebrity's party could also help. Fans can boost your fame if you've chosen the Fan Favorite perk. You can ask them to hype anyone in your household, including yourself (Celebrity/Ask to Hype). This is an easy way to build fame if your Sim has lots of friends.