1999 Ford Escort My Car wont keep a charge

Electrical problem
1999 Ford Escort

My car wont keep a charge for more than a few days.I was told if I crunk the car up and unhooked the battery and if the car cut off then the problem would be my alternator. Sure enough I unhooked the battery and the car cut off. So I went and had my alternator tested and they said it was giving off a charge and I also had my battery tested and they said it was fine. But if I drive it for a few days the battery light pops back on and eventually the car will cut off and wont crank unless I get the battery recharged.I also recently just purchases a alternator from a place called pull a part and its stll doing the same thing.I was wondering if this does sound like the alternator is there anyway I can get it fixed without buy a whole new alternator or what. Or if it isnt the alternator what should I do?
Please help