i actually have had this problem with my aquaclears. if you read the paperwork that comes with it, it basically says that running it dry can damage the motors. so yes, a power outage could be a problem. one drawback to aquaclears. but man are they quiet and do the job. what i do when it doesnt start back up: i empty it, take the motor off, pull out the propeller, rinse it, put it back in the casing, spin it a bit, put it all back together, fill with water until it spills out then plug it back in. i sometimes have to do it coupel times before it kicks back in. what i've started to do, if the intake is pretty clean (sometimes it gets gunked up), is just leave it running but only change out enough water that the end of the intake, with the openings, remains about an inch below the surface so i don't loose suction (dyson anyone?). that seems to work.
if you do find the motor just wont' work no matter what you do, it may have burned out. you can buy replacements.