I'll correct this slightly to say this is the way the older versions of Android worked. I don't recall exactly when it stopped, but I think it already wasn't working that way when I had 2.0.
I agree it's annoying and I realize you have a tablet so updates to later versions of Android are unlikely. My solution was to get a micro-sd usb adapter and use that to copy files to/from the card.
I don't know if that would be more annoying than mounting/unmounting with buggy drivers.