I have come across a few times where Veeam has problems writing to a tape,
I have opened a support case [ID# 00832713] and they recommend submitting a feature request to change the tape error handling.
Basically The tape job failed with Tape positioning error, all following jobs using that Media pool failed also, because it keeps trying to use the same tape. I formated the tape and the jobs then ran ok.
Tape error handling needs to be improved so that one tape error does not affect all jobs and it will try more than one tape.
Also tape jobs do not have any option to retry if they fail.