I would jump the battery and hook up a trickle charger. I replaced my OEM with a Optima Red Top. It cost only $15 dollars more than stock and IMHO a better battery. One downside is that the post don't match up on the battery cover holes.
I don't drive mine in the winter. and for the first time, a month or two ago, I noticed my battery was dead every couple weeks. Since it's an '06 with the original and 24k miles, I figured I would just replace it. I got the Optima red top #78 and it fit fine. You need the #78, just 78, no dash anything (ex 78-xx). The posts line up perfectly. I think it's a hair taller so the cover is a little tricky to put back on, but it does fit. It holds a charge just fine now, no matter how long I leave it between "starts". I got mine at Advance when they had an online coupon.
BTW, There is another "Battery" thread that spells all this out. I recommend searching for it. It has pictures and everything. Good Luck!
Make sure that trickle charger has some form of a "smart charge" mechanism or other system that allows it to "float" the charge. A constant 2v charge 24/7 is just as damaging to a battery as continually draining it. I use two Black and Decker SmartChargers. One on the GTO, and another that I cycle between a couple of spare batteries for other vehicles I have. These chargers use that smart system to only run the trickle charge when it senses a decrease in battery voltage, and then shuts off once it tops it off. It repeats this cycle as needed.