My guess, and its a just guess is theres a problem with the alternator. Its stopped charging the battery, and supplying electrical power to the rest of the engine. When you jump it you put a little charge in the battery, which keeps it going for a minute or two, then it runs out as the alternators not working. I could be wrong though. Alternators do fail occasionally.
If it is the alternator. If you have a battery charger, you could out the battery on that overnight, and it might give you enough battery power to move the car a short distance the next morning.