I have an SQL 2008R2 database server with 32 databases on it.  My backup
job crashes like this after the first database is successfully backed up:

Beginning full backup for database Application_Registry_Service_DB, 1 of 32.
Full: 0   Read: 3232256  Written: 3232256  Rate: 2,452.60 Kb/Sec
Full: 0   Read: 3234560  Written: 3234560  Rate: 2,061.85 Kb/Sec
Database Object Name: 20170525132822\0000040C
Backup of Application_Registry_Service_DB completed successfully.

It even exits with errorlevel 0, but does not continue on to the next
database, and never finishes up the summary log.

If I exclude that database the same thing happens on the second database.
If I exclude the first two, it crashes on the third, etc etc.   If I try
these in the GUI, the GUI crashes at the end of the first backup.  I have
already updated to the latest clients I had around:
BACLIENT 7.1.6.4
TDP SQL    7.1.6.2

Does anyone have any insight on what might be happening? The windows event
log just shows a successful backup of the first database and no errors.