Question: One of the rooms in my house has a 20A circuit. I plugged an 11A device to one of the receptacles in that room for the entire day. Walked away, came back and that device was powered down. I connected something else to the same receptacle to test it and the receptacle is dead.

All other receptacles in the same room and on the same circuit are working fine.

Is it possible this receptacle (120V, standard US) has its own fuse, and could that fuse be tripped by a device running constantly but without apparent fluctuations in current draw?

Answer: 
I'm new to the US and wasn't aware of the fact that in many houses the light switch on the wall actually controls one of the electric receptacle in the room. It was just off.
It would be unusual for a US receptacle to have an internal fuse or circuit breaker, although if it was a GFCI outlet (the kind with the "test" and "reset" buttons that you see in kitchens and bathrooms), it could've detected a ground fault and shut off. (It's also possible for several regular outlets to be wired to a single GFCI outlet, so check any nearby GFCI outlets to see if they've been tripped.)

It sounds like you went to your circuit breaker panel and checked that none of the circuits are tripped, but you may want to double-check that. Even if a device is on constantly doesn't mean its electrical draw is constant. E.g. fridges and air conditioners are highly variable in their power consumption from minute-to-minute. (For that matter, anything with a motor like a fridge can nuisance-trip a GFCI outlet...)

I suppose it is possible that you had excessive current burn out an old outlet or a bad connection. You could take the cover off the outlet to look for any signs of smoke or burning that might accompany such a failure.

If you see no signs of electrical damage and can't find any circuit breakers or GFCI outlets that are tripped, I would say you should replace the outlet.