Perhaps Twitter has additional security around his account? An IP whitelist? Perhaps the President has a special version of the twitter client that includes additional authentication? Twitter is no fan of the current president, but it seems plausible for national security reasons.
I like to imagine that it would trigger some kind of alarm at the CIA/NSA/FBI and have drones surrounding the person's house within a few hours?
Surely a hack of this magnitude would be on the radar of many of those agencies already.