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This problem still exists. The current Dreamhost advice is to "optimize" my website so that the backup file size is smaller and timeouts do not occur while the backup is being performed. Either that or turn off FastCGI. Both of these are not really solutions since (a) I can't just cut down my site content to make backups faster (that is the ultimately stupid tail-wagging-the-dog suggestion), and (b) I use other plugins and features that require FastCGI. 

Seeing that this hasn't been resolved in a YEAR, it looks like I will be switching to another backup solution, probably UpdraftPlus, which I use in some other sites without any such issues. That is really a shame because Dreamhost includes Total Upkeep as a standard, supported solution. But what benefit is that if it fails on a normal-sized site using default settings?