where are you checking the output voltage at?
if you are checking it at the battery try checking it at the output terminal on the alternator (the large terminal on the rear of the alternator) where they #10 wire is connected to.
If you still do not have voltage output of at least 14.2v then the alternator is defective.
In my experience on these mitsu/cat trucks generally when the battery dies or the truck gets hard to start due to low battery voltage and it is related to the alternator output it is related to the wire and the fuse links (and or the disconnect if it has one).
Check the output at the alternator and again at the battery and see if there is any voltage drop, usually there is, if so check the fuse links inline on that battery wire, there should be 2 of them. The connections are bad about corroding up and interfering with the charging of the battery.
If by chance you have a battery disconnect switch on the unit you should check the resistance across it to see if that is effecting the charging. If there is a battery disconnect switch it should be a black box located on the left side of the truck behind/beside the battery.

good luck