Pets never stop eating
2004 said
A happy pet does 125% damage. An unhappy one does 75% and starts to lose its loyalty.
Forever says
Blizzard hasn't said whether pet happiness returns. We're testing it in the beta.
The hunter chapter gives pet happiness three levels: happy at 125% damage, content at 100% and unhappy at 75%. Let it stay unhappy and the pet thinks about leaving. There is a warning box about how much a pet eats.
Blizzard's hunter post for Forever doesn't mention happiness at all. Rambleon is checking it in the beta, and this entry will be updated with what we find.
A hunter's pet is an animal you tame in the wild. It fights beside you and keeps the enemy busy while you shoot.
Where this comes from
How we verify- The 2004 guide
Happy 125%, content 100%, unhappy 75% and losing loyalty
Read from the guide, printed page 102 - Not confirmed
Whether pet happiness works this way in Forever
Blizzard's hunter deep dive doesn't mention it.

More from this chapter
Changed in ForeverHuman hunters and five other firstsHumans can be hunters too. It's one of six new race and class combinations.
Testing in betaThree bags, feeding twoBlizzard hasn't said whether quivers and ammunition return.
Changed in ForeverHunter, then and nowAimed Shot for every hunter at 20, traps usable in combat, pets that scale with your gear. The dead zone stays.