Apologies for the thread necro, but I figured I should give a final update.
Was all ready with Wireshark, and waiting for the problem to happen again - but it didn't. And four months later, it still hasn't happened. Everyone seems to be working fine. And I still had no idea what the problem was, or why it suddenly vanished.
It could be sunspots for all I know. Thanks for all the advice and suggestions.