04 Mustang GT having trouble holding a charge

Hey guys I have a question that has me
stumped. I think it's the charging system,
at times while my car is running my battery
light will come on and drain my battery
until my car stalls out or sometimes the
light will flicker on and off 5-10 minutes
apart. At other times the light is off and it
runs great. Is this an altanator problem?
There also has been 2 occasions where my
car was parked and not running at all but
my battery was still dead when I tried
starting my car. Is this due to maybe
something drawing power and eventually
killing my battery? Please help me on this
one! I also had the battery and altanator
checked and was told that both passed all
test. Also These test were ran without the
battery light being on and while the car
was holding full charge. Thank you for your
help!