The battery gives the starter the, umpf! it needs to turn over the motor and start. As soon as your engine starts the alternator runs all of the electrical on your car. It also keeps your battery charged for the next start. If the alternator isn't working fully or at all, then your car will draw electrical straight from the battery; a battery not being recharged. The car will continue to run, but dies slowly along with the battery. The other writer is correct about the age and condition of your battery, that may be all it is. Check alternator when you purchase your new battery, there's no cost. Good luck!