Yes, but when you're copying you're likely doing so from cached Rigs because they're already-loaded. I'm guessing that this is why the app takes a while to load - it's dependant on the library size and the time it takes to load it into RAM. When you come to paste, the app immediately tries to access and write to the drive.
I'm not on Windows, but I experience this sort of thing all the time on Mac 'cause I have my drives sleep after a period of 10 minutes of inactivity. After the spin-up wait, things proceed as-normal, but as I said, it sounds in your case like the app's either having difficulty accessing the drive or finding the correct file path to write to.
Would you be willing to try disabling any auto-sleep settings? If it makes no difference then you could turn them back on, so no loss.