Yeah, sometimes PSP Video 9 doesn't recognise what drive the PSP's connected to.
All you need to do is to find out what drive your PSP is connected to (check this on My Computer: put your PSP in USB mode and it'll say Removable Disk (drive letter)). Then in PSP Video 9 click on the setup tab and select which drive it is from the PSP Drive drop menu, and press save. Now when you click on the copy tab it shouldn't ask you to connect your PSP to your PC.
Hope that helps.