Having now got (mostly) to the bottom of this failure with Support, I'm posting this just to let other users know and hopefully avoid....
What happened was, using the DH Panel "Edit Addresses", I viewed one address and then used Back to return to the previous one to to change the disk limit.
Big mistake. The Panel overwrote the settings of mailbox A with B's, and deleted mailbox B and all its messages. Support tried but were unable to recover the messages from backup.
As Torben said: "Learn this and avoid serious mistakes: never use the browser's back button while working with the DH Web Panel!!"
Since then DH have fixed this particular failure point but recommend that given the way the panel is coded (storing variables in the browser rather than each page), never to use the back button unless you reload after, and never to use two browser windows on the panel. (Presumably never use bookmarks, multiple browsers or indeed multiple simultaneous users either.) And said they'll work on making the panel more navigation-proof.
This has been a PSA.