I don't think anything happens. But really, if you reach that time, you should get like a event Pokemon like Celebi or Deoxy, as a reward for playing that long! LOL!
It stays at that time....however if you keep playing you may encounter shinies as your wild battle odds in encountering one have gone up if you haven't encountered one yet. That has been my experience. If I was to get an event pokemon when the time reached that point I should have a one in each game. My time is generally generated in training and berry production, not in actual game progression.