Some more information. After generating some huge files, it appears that Windows Backup has particular difficulty with files around 151GB in size. I haven't managed to track down the precise threshold size when the errors start, but it's somewhere between 151GB and 155GB.
Obviously it takes a long time for me to generate the files and test the backup process (pretty much only 1 per day), so if anyone has a similar problem or can reproduce the error, I'd be interested to hear of it.
Thanks,
Andrew