The PSP got off to a weak start because of its high price and weak support. The rise of piracy shortly thereafter convinced publishers to avoid what was already considered a rather weak platform. This created a software glut that lasted years, and didn't begin to end until just this past year, after Sony worked out deals with various publishers to return to the platform. Things for the PSP are starting to look up, but it's arguably too little too late.
That being said, the PSP is doing quite well in Japan, where it had a resurgence of sorts around the end of 2007. The Slim, Monster Hunter, and Final Fantasy have helped the PSP to be a strong contender in that region. The willingness of Japanese consumers to spend plenty of money on material goods (they sell anime on single DVDs that contain a mere two episodes - for $50 a pop, $80 for Blu-Ray) has also helped to keep piracy low in the region, compared to North America and Europe.