That sounds like a charging issue. The most likely culprit would be the alternator. Has the battery warning light come on while you're driving? Are the headlights dim? What happens if after you've been driving for a while you shut the engine off and start it right back up again?
Unless there's something in the the car staying on after you shut the engine off, like some little interior light, digital clock, or something, my first instinct would be to check the alternator and all the terminals on it that lead to the battery.