This problem occurs on loads of PSP's, it's kinda common. Before making it into a hardware problem I suggest that you try Joysens. With this you can configure to analogue to make it go to the center. It worked for me when it was not working correctly on mine, now it works like a charm.
If that does not solve your problem, you'll have to go inside the PSP and clean it or something like that, I don't really know that much about the hardware stuff. But it should work.
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