Getting 'signed out' after exactly 1 minute of inactivity
This was related to the place that the sessions were being stored with my hosting company (Vidahost). Using the Utils section in Craft2, we managed to track it down to being stored with memcache. This meant that true and auto wouldn't work, and we had to set the override to false. False is meant to be the default anyway, but it seems to be working now that it's hardcoded.

The key lines to look for when debugging this are:

session.save_handler    memcache
session.save_path       tcp://10.168.1.55:11211?persistent=0&amp;amp;weight=1&amp;amp;timeout=5&amp;amp;retry_interval=15`