problems with my neon....

I have a 97 neon and the Battery went dead the other day. So i went to my local parts store which is auto zone and got them to test my battery and alternator. They tested the battery and then the altnerator and the problem was the battery so I got An Optima red top. And coming back from a vacation for one week i go to start it and its dead. Takes a jump right away and off i go. It works fine for about another week and then i have to leave for a week and when i get back it wont start again. Just wondering on anyones input. Thanks

You can check for a couple of things; any small lamp that is left on can drain the battery in a few days. Like an underhood light that doesnt turn off, or the trunk lamp, even the lamp in the glove box if you have one (our Neon doesnt). You can check whether the alternator is pumping out energy by starting the car when its dark outside, and turning the headlights on. Leaving the headlamps on as you shut the engine off, the headlights should dim slightly, not much. If they dont dim at all, then the alternator isnt doing its job. If they dim a great deal, I would suspect you have a bad ground connection somewhere between the negative post on the battery, and the body of the car, or the metal of the motor.
It is possible for the terminals to have a coating on their inner surface that results in a poor connection to the battery post. Before I put battery terminals back onto the post, I always scrape away the oxide and crud with a small Exacto knife or pen-knife, from both the inside of the terminal, and the outside of the batttery post.