Normally there is no copy protection on a PSP memory card (that I am aware of). If you are having trouble copying files to your memory card - check the memory card itself. First check to make sure there isn't some kind of write protection switch on the card (there usually isn't) or damage to the card. If you are still having a problem, you should try to write to the card using something other than the PSP (like a memory card reader). If you ARE able to copy to the card normally via a card reader - then try re-formatting the memory card on the PSP and try again. Hope this helps.
There is another possibility that the card attributes were somehow set to read only (I'm just thinkin out loud here....at 3am). You can check that by right clicking on the root directory in the card and checking the attributes.