This is something I discovered with a psp equipped firmware 3.00 (I bought the camera to use it with the firmware) I had. I found out that when I visited a website such a en.wikipedia.org and did a search, my PSP would shut down on it's own (not sleep mode).
The PSP would try to load the "Search Results" page, and when the first chunk appeared, that's when the shutdown would occur.
This lead me to believe that there was a memory overflow with the browser, and yes it was corrected by firmware 3.01.
I think the PSP firmware is equipped with what you can call a memory overflow "breaker switch" that shuts the system down when an overflow occurs to prevents exploits from functioning.
The PSP has the TA-86 motherboard.
Unfortunately the PSP in question got wet, and the memory stick access light is stuck on ON. Luckly for insurance, I have a replacement.
I may be wrong, but I believe that this is the so called "security update" Sony had states during update.