Have you tried opening it up to see if it's just loose? I have no experience with the USB port, but I have opened up my PSP for repairs a bunch of times and I kind of remember how the USB port is in there. If you can open it, maybe you can fix it too.
The bad news is, if it's broken, you either need:
Soldering skills and a new port....
Mini USB Connector Manufacturers & Suppliers
A new PSP motherboard
or a New PSP...