1996 Ford Windstar, 172Kmiles, 3.8 engine

Who told you the alt is "sucking" juice from the batt? The alt charges the batt when needed as determined by the voltage regulator, usually located within the alt. Old time generators charged and decharged as needed. When the car is running and all is working fine, the alt keeps the battery charged while also supplying power needed for car usage. If the alt fails, the car will run only on the battery, the term " reserve capacity" which is noted in minutes, such as 120 minutes or whatever, is the approximate length of time the car will continue to run, with minimal accessory usage, until there is not enough power in the batt to run the car. That is probably why your car keeps dying off after a short period of time as the batt is not being charged by the alt. It could be the alt or the voltage regulator may be bad. Buy yourself a hydrometer, they're cheap, charge your batt up and check each cell if possible to access the cells, I never buy a battery unless that is possible. There are totally sealed batts and ones with accessible cells. If the car will jump-start and run, I would have the charging system checked by reliable garage. If a cell were shorted out already, chances are the car would not run once you unhooked the jump vehicle and may be hard to jump anyway. Just my observations when dealing with electrical, it's a maze. All kinds of things involved, check all the alt connections, look for any burned fusible links, etc. Good luck