Battery keeps dying while driving

Did you have the alternator checked while it was still on the vehicle or hdid you have it tested seperately?

Have the charging system test at autozone or advance auto [they test them for free]. This will give you an idea of how the system performs under a load.

Also, you can use a testlight to check for power ont he DARK GREEN/ORANGE wire at the alternator with the key on and while it is running (there should be power there both times). Also the DARK GREEN wire should have power [although less voltage].
The larger alternator wire should have full battery voltage there at all times.

Have it tested on the vehcile. There couse be a problem with wiring, a connection or somthing like that. It wouldn't show if the alternator isn't on the vehicle. Basically, we need to know if the system is working under "normal" conditions. Have autozone or somewhere like that to check it and tellus what the tests revealed.