Well, technically it isn't a hardware problem but society's because PSP is close to being a flawless portable gaming device, just look at all the awesome features it had:
- Fantastic graphics
- Optimum gaming experience on the go! (PSPgo is an embarrassment for the other PSPs)
- Video Player
- Music Player
- Play Music While Playing Video Games
- Watch Internet Videos
- Use PSP's screen for PC use
- Use PSP to play on a PC screen
- Backup your games to the memory card to a much smaller size
- Run games on HDD to your PSP
- UMD discs, a unique disc format for PSP-only
- Thousands of homebrew plugins/apps/games for PSP
Despite all the great success, PSP did bad due to one reason, people outside Japan were/are used to download pirated PSP games than actually buying them and showing support.
Some of those are kids whom their parents can't afford games or don't want to buy the games, or an adult got fired and can't waste money on games.
Though, PSP games have gotten relatively really cheap, just look at this: http://amzn.to/H2JUtz
My only complaint against the PSP is one, and only, it just had one analogue stick which ruined for me the experience of adventure 3D and FPS/TPS games, it's true I could get this on PSP but I'd have to pay for it to be modded.
On PS Vita they've added a second analogue stick, screenshot plugin, and whatever I can't honestly remember, I see that Sony has looked into PSP's Homebrew Community and made use of that info for PSV's software device.
By the way, while I'm ontopic, my nephew's PSP 1000 (it's hacked) I played Dragon Ball Z: Tenkaichi Tag Team, and wow! It's SUPER-EPIC-FREAKING-AWESOME!!
I bought the game after playing the pirated version even though, currently, I don't have a PSP to play with, but I'm a big fan of Dragon Ball Z.
Lastly, don't get me wrong but I'm planning on buying a PSP Slim (2000) that hackable so I can use the homebrew software (apps/games/plugins) because god damn, Sony's official firmware is so weak and useless.