I had the battery in my '95 Contour last about 7 1/2 years before I replaced it. My car was a Nov '94 build and I replaced it in the summer last year. It was actually fine and I didn't think it could last much longer. Got a replacement at K-mart for $45 so it was cheap insurance for the winter.
Like someone else said, 1.1 miles probably isn't enough to charge the battery and you should also check the under hood light bulb, make sure it's going off. You can also check for a current drain by putting a meter on it. Running the battery all the way down is also another quick way to kill it and those short drives are probably doing it.
