charging system woes Ford f series

my old f350 (1988) is kickin my butt. replaced alternator and all seemed fine system showed 13.8 volts. so off i went for a ride. had the lights and heater blower on high. drove about 15 miles .stopped to gas up and battery almost dead. got it running and hooked up tester all seemed fine again so i added a load one at a time. all lights on showed fine. added the heater fan and it dropped to 12. shutt off lights and just heater blower it was fine. added the lights it dropped low. alternator is new heavy duty. battery is a couple years old top of the line interstate 700 CCA. is it possible i have a dead cell in the battery thats only showing up at load? i cleaned all the terminals and post and checked for corrosion . any ideas? thanks all