this may be a strech but... check the dip tube,
the cold water must go into bottom of the heater so it does not dilute the hot water that has risen to the top, this tube is inserted in the cold inlet of the heater if it is a top fed heater.
if the tube is damaged or crushed it will cause simular problems tou have mentioned.
3 stories.. how many bedrooms, how old is the house, is there a rust problem, was the heater properley sized, and is there a circluation pump in the system?