You probably have some dirt in there under the d-pad or the contact under there is starting to get bad. Either way will require being able to pop th top off to get underneath.
Now, i only recommend doing this yourself if you are somewhat familiar with handling electronics repairs- you may be better off contacting Sony and ask them what you can do. Most likely they will have you send the PSP in for repair/ replacement which, if you are out of warranty, will cost you a bit of cash to get taken care of. I don't know how much, they will have to tell you.