Not just police and (hell-)fire:

Hospitals (doctors, nurses, technicians, ancilliaries).
Power- someone keeps the generators spinning.
Water and sewage (and gas) are mostly automated, but there are maintenance people on call.
Care workers in residential homes. And those on call for the inevitable emergencies- Christmas is one of the worst times for family break-ups, volence etc.

There are others working long and unsocial hours too: burglars and thieves, muggers, rapists. Let's keep them in our thoughts at this time of goodwill. And the terrorshits and gulag guards.

And of course, rust never sleeps.