Interesting clue that disconnecting and reconnecting the wifi connection allowed the clock to synchronise and then continue running - seems almost as if it made a connection to the server to update the time but didn't get a response. Still a bug though, as I've never heard of a failed time update on any other system causing the time to just freeze...
BTW you don't have to remove the battery (which is as you say stupidly difficult) you just need to part them. I just put a thumbnail or small screwdriver in the gap between the batteries and twist slightly.