The backups work - about half the time; i.e. I have a log backup configured to run every 30 minutes, and it's run successfully at 02:00, 02:30, then failed at 03:00 and 03:30, then run successfully five times and failed again at 06:30, then run successfully again, etc.
I checked service accounts - SnapCenter SMCore Service and Plug-in for SQL Server Service were configured to run as local system, while Plug-in for Windows Service was configured to run as the DOMAIN\snapcenter account which is registered in SnapCenter. I set all the services on both nodes to use the DOMAIN\snapcenter account and restarted them, and the next four backups ran successfully, but the fifth failed with the same error as before.
I'm not sure I can open a case on this; the old filer on which this problem first manifested is out of support, while the new system was purchased with service from an ASP rather than direct from NetApp, and the ASP claims that SnapCenter is not covered by their contract.