Sony's planned future for the PSP doesn't seem to involve a successor, with the president of SCE Europe recently saying that the company has no plans for a PSP 2. He cited several reasons why a PSP2 is not a possibility in the near future, such as game development already being torn between numerous platforms - PS3, 360, Wii, DS, PS2 and even the PSP. Another handheld console might get too little attention, which would make sales an even more difficult thing. We've all seen the criticism the PS3 has faced, a large portion of which was due to the poor game selection in the first year of the console's life.
The PSP itself has been outsold by the DS at around a 2:1 ratio, despite the PSP itself having more hardware under the hood. That's not to say the PSP isn't successful in its own right, having sold over 40 million units since its release. Sony for now is still taking a route similar to Nintendo, releasing upgraded or expanded versions of the handheld rather than seeking to completely re-engineer it from scratch. That's probably better for them in the long run, as the PSP certainly hasn't reached its limitations.