This has never happened to me too. Must be more of a data centre thing.
Anyway, thought I should chime in since any changes they make to solve this would affect me anyway. And I like thinking of ways to solve things too.
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Had this happen too, not on Bray HM mind you, but the tank threatened to leave after one wipe on Pharos Sirius before. It was on 2nd boss (Zu with the eggs) even though he's the one that for some ungodly reason destroy the eggs all the time and keep stacking enrage on Zu to the point of it spamming the ground stomp move lol.
as for 2nd boss leaving, I only had it happen once on Bray HM out of 350-360 something odd runs, so I count myself lucky lol. Is it always Tanks that leave? Honest question because I also tank 99% of the time in Bray HM (unless I got asked to help FC/LS members and they need dps/heal slot XD) and it was one of those rare times I went as dps that I got one tank that just left after 2nd boss lol.
there is an "hidden" change to expert roulette: the daily quest for the new map