Most common issues with tape devices:
1) Tape drive asks for cleaning more frequently.
2) Media will be marked as full after writing very less amount of data to it. (Will happen with all the media in the library)
3) Media requested by BE may not be inserted properly into the drive.
The first two indicates that there is a problem with tape drive. Investigation has to be done with tools provided by the vendor. Like HPLTT tools for HP drives, IBM ITDT tool for IBM make etc... Perform a write test also along with the general investigations. And some times the drive temperature also create problems. (Drive fan assembly may be having issues). If any problems reported during the testing by using vendor tools, contact the vendor and ask for a replacement.
The third indicates there may be a problem with robot. In this case you can see something like "Stow operation failed at slot XX"...