136 is kind of brutal lol I think 50ish is still my longest and that was when I first started beating Nishi using defensive/healing pets which meant vs the sunflower it was more like a healadin mirror duel.
While fighting Nishi's sunflower—who was up first—I once killed both back line pets with a Nordrasil Wisp's Arcane Explosion while the sunflower was still up just to see if I could. It took a long time, but certainly not 136 rounds long!
I should have noted the number of rounds, but alas, I did not.
My current highest was 243, a Malayan Quillrat Pup I was leveling vs Dor the Wall. His only damaging move (headbutt) is on a 3 round CD, which happened to line up perfectly with my survival. If all of my bites landed and he didn't stun me with his headbutt I would make some progress towards killing him, but if any of my hits missed or he stunned me then he would outheal my damage for that round.
Using a stall team in conjunction with Apocalypse (cockroach ability) is one of the few legitimate PvP strategies I've seen that has the potential to win. It can be countered easily, of course, but if the enemy team doesn't have any dodge/miss/reflect/immune abilities it can be devastating. With the cooldown on Apocalypse, it takes 60+ rounds for this strategy to deliver.
Oh man. Anubisath Idol vs Aki's cricket, I had the worst streak of rng. Sandstorm miss- crush miss- he can't hurt Anub through the sandstorm and all the misses were letting him heal up repeatedly. I stuck with it and finally killed him off.. the end of the battle was 84 rounds.