Ken,
I discovered I was running out of space on my server when my backups started failing. I looked into it, and it appear that they were failing because there is no more space on the server for them.
I downloaded my full website so that I could analyze the files with "Disk Inventory X" and it showed the "filedir" at about 32 GB.
Also, InMotion hosting has a neat feature called "Disk Space Usage" which showed the following:
You can also see the size of my public_html/ folder is a bit over 500 MB. I have kept the two classes I am hosting small by purposefully not uploading any video, as that has been an issue in years past. With my classes about 500MB, this should leave space for 60 or so full backups, more if they are automated backups. This appears to be what has happened.