I don't know what triggers it, but the tape library only stays online for a few days, and then Veeam says it's offline and won't talk to it. The library itself hasn't been power cycled, disconnected or had anything else done to it that would cause it from a hardware point of view.
In Veeam, if I go Tape Infrastructure -> Offline Tapes -> Quantum Scaler i40-i80 153G, right click the library and choose Rescan
It pops up the job progress window, but it just says: Tape library QUANTUM Scalar i40-i80 153G (offline) appears to be offline
There doesn't appear to be any other way of getting the library online.
Restarting the tape library doesn't help, and I can't keep rebooting the Veeam server every couple of days. The library is a Scalar i40 with a pair of HP LTO-5 drives in it, and with EMC Networker, it ran pretty much flawlessly.
Veeam is 126.96.36.1991.