Hello, and welcome to the forums.
A few things to try out/confirm (recommended for a fellow ATI card owner like yourself, and this comes from personal experience with a similar card, running PPSSPP smoothly using 11.11a drivers myself.):-
1. First thing you do is to make sure that Catalyst A.I. (also known as Surface Format Optimization) is disabled in the ATI Catalyst Control Center. Even with the 11.11a drivers installed, this setting can cause issues on ATI cards in PPSSPP if it's enabled.
2. Within PPSSPP (Settings --> System), disable Fast Memory. It's still not a 100% stable option and can still cause crashes in certain segments of certain games. It's enabled by default.
3. Just to confirm, you're not doing any form of overclocking with your ATI card yes?
4. Last thing you can try if you're truly desperate, perform a CLEAN re-installation of the 11.11a drivers. Uninstall the current drivers you've got, then use Driver Sweeper or
DDU (which is a newer and better version of that software) in Safe Mode to wipe out all remnants of any previous driver installations you may still have on your system. And then, and only then, install the 11.11a drivers again using the normal AMD setup method.
EDIT:- It'd also help us to help you if you could upload a save file/save state right before the point where the game causes display driver crashes for you. Unless of course if it happens at random.