For a week or so, I've noticed that the FT847 Power switch has been playing up a bit. I thought it might have had something to do with running off the battery and the voltage being a bit lower than 13.8v. However, it seems this is not the case!
It looks like this is a known problem!
So far, I've managed to persuade the switch into action ok, but whether it's going to end up expiring, I'm not sure.