I did a test against Watchman Prenn in Steamfont a few minutes ago. The evidence seems to show that pets do not regenerate while in combat. At least, if they do, the regeneration is nowhere near 30 per tick

The first fight was a quick check of the mob. I let the guard kill the pet, then I zoned. The guard logged 4263 damage, which is consistant with tests done by others. The kill shot did 175 damage, so this means that the pet has anywhere from 4088 to 4263 hp, including any regen over a 55 second period.

The second time I kept the pet healed for as long as I could. I ran out of mana before the pet died

Watchamn Prenn did 12253 damage to the pet in 165 seconds. I cast 11 Renew Summonings and 10 Transons Elemental Infusions. I don't believe any heals topped off his hp so unless there is a random factor to heals I don't know about every heal did full damage. If a heal did not heal for full, it was a 220pt heal. According to Lucy, I healed 8220 damage.

12253 - 8220 = 4033. Kill shot of 151 so minimum is 3883.

Possible Conclusions:

Pets probably do not have the same number of hitpoints for each summon(I'm fairly sure this is true).

It is unlikely that pets regenerate during combat. Assume there is a 30per tick regen, and assume that Lucy is right about mage heal spells. The first test would give the pet hp in the range of 3819-3993. The second test would put pet hp between 3223 and 3374. Judging by a % healed test the pet might have as low as 3800 or so. Judging by % nuked test the hp was as low as 4083.

Pet health at 3223 to 3374 does not match anything we have seen before, even a short evaluation using melee combat. Therefore, I find it unlikely that pets regenerate during combat. The only other explanation I can think of is that Lucy is wrong about how powerful the pet heal spells are.

Summary:

12253 damage versus Zartik in 165 seconds 8220 of which was healed by myself, leaving 4033 native hitpoints over a period of 27.5 ticks. This would mean that 810 of those hitpoints would have to come from regen, meaning the epic's unbuffed hitpoints would be lower than any other recorded test, even tests that totally removed the regeneration factor.