What possible problems could be the cause of the battery dying.

I have a 1997 Mercury Mountaineer and the battery keeps dying after a few startups. After a few startups I have to bypass the starter and use a screwdriver on the starter solenoid to start it. I replaced the battery, alternator (both on 7/9/12), and the starter solenoid (replaced on 7/6/12). The starter was replaced a few months prior.