It sounds like either the car isn't getting enough use to recharge the battery after start-up, or that there's an electrical 'leak' somewhere (often an alarm or a radio), or that the alternator is failing. Have you tried charging the battery? Some battery chargers will give you an indication of the health of the overall battery and its state of charge. Winter is a notoriously draining time for batteries - it takes around 70% of the battery's charge to turn the engine over and when you add all the extras on top (heating, lights etc) a car that doesn't get much use can soon have a flat battery. Equally, a failing alternator will not recharge the battery enough. As for the rough running, it could be down to a number of things - from a failing fuel pump, to poor quality fuel, debris, failing ignition system (plugs, leads etc) or even a blocked air filter.