I have noticed it too. Seems very inconsistent too, almost like the cower/charge bug or like my gorilla just standing there after a mob dies.

Hunter pets in general have just been weirdly bugged lately.

It's apparently the small amount of time when all the stamina and other 'buffs' applied to the pet by the hunter, or anyone in the party, kick in. It shows up at half health because your presence ups its stamina by that much.

Or so I've been told

Aye. Your pet has base stats, and then it inherits a certain amount of your stats to add to those base stats. This is calculated when the pet spawns (after being called, after you dismount, etc.). Once the bonuses are applied, the health total is then adjusted to fill the new max health.

There is a slight delay between the time when the pet spawns and the time when the calculated stat bonuses are applied. This delay can be exaggerated if "stuff" is going on, such as when you are in combat. In extreme, or extremely unlucky, circumstances, it seems that the process can be truncated before the final step - the addition of the new health to the pet. That is, the health bar is increased appropriately based on the stats the pet inherits from you, but the actual amount of health the pet has is not updated.