Just had the exact same problem on my Grumman AA1B (Lycoming O 235). The original 38 yr old starter solenoid had worn out and was not passing full current to the starter. You could tell it was the solenoid because you could hear it chattering. Even if it turns out to be the battery you should consider changing the solenoid while the cowl is off if it is the original one. They are not that expensive ($38 for mine) and it is a simple job.
Last edited by Big Pistons Forever; 30th October 2012 at 16:21.