Official PlayStation Blog, Sony is aware of the problem and is working on a fix in the form of Firmware 5.01 (version 5.00, which enabled the PSP to directly access the PS Store, was released last week).
No word on when the update will be available. In the meantime, if you're having trouble with the storage recognition, you can still download PSP games via the PlayStation 3 or PC PS Store, like you did in the days before 5.00 (i.e. October 13 and before).
[Via PSP Fanboy]