Your alternator could possibly be going bad as well and not charging the battery like it should. Try running some diagnostic checks on the battery/alternator to find out if one or the other is failing.
Get a voltmeter and measure the voltage across the battery terminals. Make sure you're measuring on DC scale. Ideal range is 14 volts but if you read lower than 12, it's probably the alternator. Don't worry about what's below if that's the case.
If it is still reading around 14, try turning everything on that requires power like heater, rear defroster, radio, lights, etc. and give the car some gas (in neutral). Have a buddy measure those terminals again. Voltage should still be around 14, but if lower than 13, this is again an indicator of a bad alternator.
Also, there's another step that I found quoted from another site:
One last failure mode is of course noise. The rotor inside the alternator rotates on bearings, normally very high precision needle bearings, and these can fail. When they do you will hear a loud grinding noise associated with the alternator. To isolate the noise take a length of tubing, heater hose will do fine, put one end to your ear and move the other around in the vicinity of the alternator. The noise will be much louder when you point it at the alternator if that is the culprit. Other possibilities are the water pump and the power steering pump which are also driven by the engine belt. To further isolate the noise disconnect the drive belt and spin the alternator by hand. If you hear a rumble or grinding noise then the bearings are shot. If you don't hear a noise the problem may still be in the alternator since the bearing might be quiet without the loading of the drive belt tension. Check for side play in the pulley. If you are pretty certain the noise came from the alternator it is a relatively simple task to take it apart and visually inspect the bearings, else swap it in for a rebuilt. Your auto supply store will normally bench test the alternator free of charge and can tell you at that time if the bearings are noisy.
Hope that helps..