1988 Oldsmobile Ciera Cranking and Jerking

Car sometimes will not crank after a day of using it. The car has had several boosts to get restarted over time but with everything off sometimes it goes straight back dead. Dont know if its the starter or the battery. Alternator has been recently replaced so know its not that. If u so much as even get out of the car and left your headlights on with the car off even for a min or 2 the car will go dead. So something is bringing the battery down but dont know what. Also driving down straight highway the car will steadily jerk as if tho its running out of gas like it is sputtering. No one can tell us what the problem could be exactly. Dont know if the motor is on its last lega or what so can u pls help us?