Did you ever find a reason for this? I seem to be having a similar problem.
I'm not sure if it's coincidental, but shortly after I updated to 14.0.4 and 14.0.4a (I did them both at once), my server started hanging after some (not all) backups. I have both my data and backups on an external RAID6 box connected via Thunderbolt2 to a Mac Pro (Late 2013) running 10.10.5.
It only ever happens at the end of a backup, and so far it has only happend with backups that do the "Verify" step afterwards, the Consistency Check. Toward the end of the Consistency Checks for all databases, it the storage hangs. Sometimes it comes back after awhile and things continue where they left off. Other times it doesn't come back and I have to force-restart it.
I first suspected the RAID6 box, but I've been working with the vendor's support and all seems to be fine. And it's very suspicious that this box goes nuts with constant normal I/O all day and night, but the only time it ever hangs like this is right at this exact moment in the FMS backup's consistency check, every single time.