Battery trouble in 2000 Mustang

Alright so a few months ago I went to start my car and it had zero power. We tried to
jump it but it would only make a clicking noise, the engine would never turn over. So
we got a new battery thinking that was the problem and it has worked fine. Now two
days ago I was leaving work and the car would not start again, no lights came on,
nothing, zero power. We tried to jump it and it did the same thing, made clicking
noises. We adjusted the connections on the battery and it started right up. Then a day
later it happened again. Our neighbor suggested changing out the connections so we
did, but it still is not working. Anytime you try to start it, it has zero power. If you hook
it up to a car the lights will come on, you turn it all the way and it just clicks. With a lot
of adjusting of the connections we can get it started but it takes about 20 minutes of
trying.

Does anyone have a suggestion on what we can try next? Like I said the battery is
only a few months old, it has not been really cold or really hot. Any help would be
appreciated!