If Nintendo itself if fighting with teeth and claws to keep its handheld market from shrinking, Sony won't be interested in the efford. The Vita will probably last a long time, because its pretty powerful already, but Sony will not invest in more gaming handhelds when they can just use its mobile department for that.
The PSP was victim of its own hardware. It was a very powerful and advanced handheld for the time, in a moment before tablets and smartphones could really compete in the multimedia department. Also, really easy piracy sold a ton of units too. The Vita has neither of this things, and I don't see how its "successor" could improve on that.