My games do not finish Saving

[LunaMoo]

Just because you used both savestates and savedata for long time before and it worked together, doesn't mean it's not the case [Unknown] linked, many games have built in protections and check for previously written savedata comparing it with memory state. In which cases if you load savestate made before last save data, you're telling the game "this savedata is not mine" and it reacts with "I'm not going to allow writing over it".
The way to solve it is simply restarting emulation and loading last proper in-game save, forgetting about savestates you desynchronized by your "time travel".

To list a few other cases ~ cheats, mods, unsafe/experimental/hackish settings all of that can also cause random problems including saving ones, in fact no game is 100% stable to play without restart forever even on real psp, it's fairy common for console games to have memory leaks and other minor bugs that can accumulate over time completely breaking things and abusing emulator feature like savestates simulates exactly that - playing for very long time even days without a break.
And again in most of those cases even if caused by setting you disable later, you will have to forget about savestates that are already affected by issues and restart emulation reloading last properly made in-game save.

So to be safe and test all of this at once, restore default settings(we have an option for it in system settings) then forget savestates even exist, restart emulation and reload game from in-game save, then go to any place where you can save and see if it works properly again.