@mmn Hmm and if I try to install Debian Jessie I get the same error on a completely different machine even if the same drive's not plugged in... (and sort of this error - unannounced shutdowns - started showing up when I updated it to Debian Jessie, but then only during the nightly backups).

So I'm thinking kernel issue. Will try to install Ubuntu, which seems to work on another machine from the same batch.