Pet Regen Cap??

If there's such a cap, it hasn't been found yet that I've seen.

With Ecliptic Attrition up perp cost being -30 per tick, you would be recovering HP 6 hp/tick with +36 pet regen. So yeah, should tick up not down. IRRC the luopan's HP will hang at 99% since the HP is ticking up, then down every tick.

Keep in mind that Luopans have a hard 10 minute time limit. They'll depop even at full HP after 10 minutes. So you can't keep one up indefinitely, but you can certainly keep a luopan up for 10 minutes with BoG and EA up with enough pet regen. At which point, recasts are back up, rinse and repeat.

The issue there is that on most content the luopan is going to take dmg. Thus the perp- isn't the only thing to worry about. Fitting in pet DT is a valid concern.

If one were to see if a cap were attainable, it would best be done in either Reisenjima with the COR Regen roll or in Abyssea with Regen Atma's since they carry over to pets. Same for Reisenjima buffs.

Back before SMN Burn was a thing, my shell would SATA+WS burn Erinys. I would easily rock a 10 minute BoG+Ecliptic bubble and didn't even have to watch it. It stayed at full HP between my gear and Reisenjima buffs. It was the most boring fight, but easiest of them all.