Frons went to the wall to try to save first Guza, then GH in 2011 from the ax IIRC. He felt Guza was GH's true north, that only he could write it. But he couldn't protect him after a certain point, and he was gone not long after himself.
I think JFP stayed on because she was a capable line producer, and because after Guza's grand return with Frons' blessing in '02 and her complete disaster stint with Megan McTavish the previous year that was largely what she was reduced to. Guza had learned from his battles with Wendy Riche and came back with a co-producer credit; he had creative control (beneath Frons), which was unheard of for anyone other than JFP in the mix at that time. And she lost it all. Based on the difference between her past work at other shows and at GH post-2001/early '02, it appeared as though Jill never had real creative control (outside of the '08 WGA strike) at GH again. And she deserved to lose it. She was reduced to getting her ex Kale Browne constant voice-over gigs on the show because he was widely disliked among performers and production across ABC (Hillary B. Smith and Mark Derwin were still taking anonymous shots at him in the OLTL oral history, and he was fired the instant she moved to GH) and she no longer had the power to force him onscreen.