When the crew became cursed for stealing the Aztec treasure, the monkey also became cursed (undead) as well for taking some of the coins.
Hector has the pirate player use Jack for target practice when he first shows them how to use a pistol. After all - the cursed little monkey can't die no matter how many times you shoot him, or attack him in any way, with any weapon.
Note: A way to reduce his health to zero is to use the "life drain" voodoo doll skill on him. Even though it says he has been defeated he will remain in place until enough time passes for him to respawn. (this might take a while for him to respawn)