I don't know if this can help but the PSP crashed on me a few times while playing descension tournaments, usually at the end of tracks 10 to 12. I realised I could avoid this bug by waiting a few seconds each time a stats screen ("stats screen", yeah?) appeared, before pressing any button to go to the next screen.
If you want to PM me your profile I could play the ascension tournament and tell you if it went right or wrong.