I got the same kind of problem before, when my 4GB MS Pro Duo suddenly corrupted (since it's a Class A product) and decided to reformat using the PSP's "Memory Stick Format" option under System Settings.
But after formatting it and put some games on it, some games (ex. DJMAX Portable 3) tend to freeze and my PSP turned off all of a sudden. I tried loading the game again, but still freeze and my PSP turned off again.
I tried reformatting my 4GB MS Pro Duo from my friend's PSP. I tried loading DJMAX Portable 3 and got surprised that it loaded just fine and even played a couple of songs.
I just bought a new 8GB MS Pro-HG Duo HX, and formatted it on my PSP. I copied all of the files from my 4GB MS Pro Duo already backed up on my PC (since my saves are all there and don't wanna end up my MS corrupted and losing all of it again), and copied some games. I tried playing Gran Turismo and it works just fine, but when I tried playing DJMAX Portable 3, "the freeze and PSP suddenly turn off" problem happened again. I suspected that my PSP, although it formats my MS Pro Duo just fine, is the culprit. Or maybe the CFW is the main culprit.
Anyway, since my friend who got a PSP that has a working MS formatting isn't around, I can't play some games on my 8GB MS Pro-HG Duo HX. SO I need to find an alternative: formatting it on my PC. So I formatted it using a cheap card reader, copied all PSP files and loaded DJMAX Portable 3. The freeze seemed to be gone, and the game successfully loaded and got past the intro movie. I even played some songs, and it still works just fine. Problem solved!!
So I suggest that:
1) format your MS Pro Duo or Pro-HG Duo HX on your PC using a cheap card reader (or use an original MS Pro Duo USB adapter which sold separately or bundled with a MS Pro Duo, just to be safe & sure)
2) use these settings when you format your MS Pro Duo:
File system: FAT32 (formatting it using NTFS will render your MS Pro Duo useless on PSP)
Allocation size unit: 32 kilobytes (I tried formatting my 8GB MS Pro-HG Duo HX using "default allocation size" which is 4,096 bytes, it works fine but the games seems to load slower and sometimes lagged on some games)
I hope this will help solve your problem, guys.
EDIT: Oh yeah, I'm using a 6.20 Pro VHS CFW on my PSP-2001 unit.
EDIT #2: Just got the dreaded "freeze then PSP suddenly turn off" crash problem after playing Gran Turismo and decided to play DJMAX Portable 3 for a bit.
After a few attempts on reformatting yet the problem still remains, I went on removing the save files. It worked and runs fine again. Then I put the game saves back, and it worked without any problems.
I suggest that you back up all of your save files/folders from your MS Pro Duo temporarily on your PC, run the game that crashed to see if it runs fine. If it is, then put back those save files/folder you backed up on your PC to your MS Pro Duo.