We have put a charger on the car and the charge holds while the car is off. But when driving the car the battery drains in less than an hour. The alternator has been tested and shows to be good. The new battery has been tested and shows to be good. The head connectors for the battery have been changed. The problem is still occurring. What could the problem be?

You almost answered your own question. The fact of the matter is the battery is draining because of *lack of voltage. And what provides your battery with a re-charge of voltage? Your alternator.

How did they test it and what did they tell you? It’s pretty obvious it’s not charging between 13.5 - 14.0 volts with the engine running. Essentially the battery is used for starting, playing the radio with the engine off for a short period of time and four way-flasher use in emergencies. The alternator on the otherhand provides amperage to every electrical circuit in the car when the engine is running.