I notice this pretty much every time ever since, well, ever.
A wild guess would be that your pet receives some contribution from your stamina. Let's use some fictive numbers for simplicity:
Pet without stamina contribution: 10,000 health.
Pet with stamina contribution: 15,000 health.
Your pet's total health pool would be 15,000 health, but due to programming, glitching or whatever, when it is summoned, for a brief moment, it has 10,000 health, before it receives the final 5,000 contributed by your stamina. The total health pool still shows because the game remembers it, so you'd have a pet with 10,000 out of 15,000 health.
Since health doesn't regenerate during combat, with too much server lag, your pet won't regen its health before the 'combat - no health regen' mechanic steps in.
Again, just a wild guess, but I've seen this happen to my Hunter's pet as well.
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Please "talk up" if your comprehension white-shifts. I will use simple-happy language-words to help you understand.