This, as far as I know, is a problem called by the ultimate tier pet talent (Wild Hunt), which is, I believe, only applied when the pet is summoned. Yes, all of the hunters specced into Wild Hunt have this problem. Those not specced into Wild Hunt still do because they are doing something wrong with their pet spec and have naturally low HP lol. I do not think there is any solution for this. However, since in arenas, pet do not disappear even when mounted, you may want to enter arena with a high amount of pet HP or heal it up and the pet is still out when you are mounted. In BGs, the best you can do is Mend Pet every time before you mount up so when you dismount, your pet still has ticks of mend pet going on. This is a problem, but hey, you can use those free cotws and furious howls once you dismount. :P