Automatic backup turned off by something

I use auto backup at 3AM every day. It works great for about a week, and then announces that the backup failed. When I click on the 'more info' popup, it says that automatic backup is turned off, and forces me to do a first complete backup again, which will thereafter allow the automatic to work perfectly for about another week or two, folllowed by the 'failed' message, etc. The backup is done to an external which is permanently attached and online and has excessive space for the backup. ONE THING! There is a lot of data. The original backup takes 4-5 hours, and the add-ons only about 30 minutes. It seems that (although there are 200GB free space) the backup sets which remain after the failure always have around 34 to 37GB size. Could there be some size limit that is forcing the new set?

There is no error in the execution that I know of, it's just a nuisance to run the new set.