2 Answers

First of all, how old is the battery? you have a parasitic draw on it somewhere. If the battery is a few yrs old and has sit what is the voltage at the battery posts while running should be around 12.6 to 13.4 volts if not your not getting a sufficient charge. Why? a diode in the alternator could be going out? could be dirt or corroded postes not permitting or accepting the proper charge. You might not always be able to see the corrosion  so clean the cables an posts and again crank her up and check the running voltage at the posts. 12.6 - 13.4 vlts could be a starter or solenoid going out drawing way too many amps depleting battery storage capacity upon shutdown. Could be an internal battery cell going bad. If you take it  to Oriley's, autozone or some auto parts retail store they will usually check it free but they are in the business of selling batteries get my drift? 

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!