There's always a percentage of consumer electronics that just fail for no good reason. Just bad luck of the draw. I hope you took it back and got another one.

I've had my PSP since 2005, and while it's probably a different model from the one you had 'for a month', I have had Zero problems with it.

(SPOILER)Also, your posts elsewhere lead me to believe you may be running Custom Firmware, which could be causing your problems. Research the latest news on firmwares and stuff and sort that stuff out.