If your alternator is not keeping your battery charged, either the alternator is bad or the battery is bad. (Unless you are storing the car, of course.)

Replace the battery and while you are at it, take a good look at the battery ground cable - when I bought my 05, in 2010, the ground cable had corroded and almost broke off at the chassis end. A new cable was $10 at O'Reilly Auto Parts.

Cleaning up the battery cable clamps and treating them is a good idea as well.