After using the experience boost and hunting for 10 minutes, I came back and found it dead.
The experience boost lasts for 10 minutes, but isn't it an error to starve to death during that time?
Digimon get hungry when battling in the Digital World and challenges. Always check the small "meat" icon that appears under the Digimon's healthbar and to go back to the lodging and feed them.
The next update will have the icon shake when the Digimon is starving. Should make it easier to keep track of things.