Version number is 11.1.6.55604.
I'm not on site so I'll have to wait until the next time I'm there to check Windows event logs. I am able to see the log files (from the day before, by looking at the backups themselves) and don't see any glaring errors there. I do see "AM High Priority Warning: Result (0xece30066 33 NOTIFY_ERROR_EVENTLOG_OPEN_FAILED Args [0];)<9 1.0-*-*-* > 0x80020009 (Symantec System Recovery)" listed quite a few times but I don't think that's pertinent since I see that same error on other working machines.
As I mentioned in the initial post, the machines are configured to keep three recovery point sets, and to start a new set each month. For the problem machines, we now have three full sets that were all created one after the other on subsequent days. What will now happen is that it will start doing increments from here forward, but when the next month rolls around I *think* it will start this whole process over, where it does three full backups in a row. It's like it resets the "number of recovery point sets" counter to 1 at the start of each month. It then does three in a row, does increments for the remainder of the month, then restarts again from scratch each month.
Any ideas what might cause this? I'm going to be going on site in the next few weeks. I'll delete and re-do the backup jobs on the 4 affected machines to see if that fixes anything. I'll report back if it does. If anyone has ideas in the meantime about what might be causing this, I'm all ears. :)