Hi JR,
Is Removable Storage disabled? If not, I'd suggest starting by stopping the service and disabling it.
Next up would be to try a small backup-to-disk to eliminate possible software issues. if it works, the problem lies with your library. If not, it's the software and we can take it from there.
However, you can also look at making sure you have the latest drivers for your version of BEWS, as well as making sure the software is patched and up-to-date.
What make of library is it? If HP, get hold of HP Library and Tape Tools (HP LTT) which will allow you to run diagnostics against the device, and update the firmware if necessary too.
Post the results here...
Laters!