1987 Mercury Topz Battery keeps going dead

I have a 1987 Mercury Topaz and the battery keeps going dead. I have a new alternator in it as of yesterday. I also have a new battery in it as of a few days ago. It starts fine I can drive it to the store and it might or might not start again.. I put the battery on the charger and it has lost most of it's charge. At the auto parts store they checked the battery and said it is fine then they checked the alternator and said to replace it...Lifetime waranty and no problem the new one is in. I have not tested it since the new alt was put in it but I drove it around today and still have a dead battery. What could be running my battery down. It is not happening when it sits still I can leave a battery in it and it will not drain seems to be when I'm driving it. Any help will be great