Why do I have to reboot to use the USB ports?

[minesheep]

It does appear that as long as I keep that Admin window open I can copy files to the drive, even if I can't copy them via a non-admin window. So for me, that seems like a workable solution.

Thanks!

Why to not fix it permanently via the administrator window

If you can access the drive with root account in thunar right click it again and select "Properties..." and allow write and read permissions from "Permissions" tab. Now it should work until you format it again.