Monk's have a self hasting ability that drains a percentage of health while it is active. This isn't as noticable when out of combat but once combat is engaged your in combat health regen suffers. It was called everburning or something like that, but since the revised combat/spell names I am not sure what it is called.
Also monks and bruisers alike have a combat art that drains health instead of power, but since a bruiser does not get an ability that enhances auto attack while draining health their in combat health regen will not suffer as a monks will.
My friends monk suffers that same scenario as you have now. He will cancel everburning when soloing and even when tanking because he says his health goes down fast and takes forever to regen. He uses everburning when in groups and not tanking.
This may not be your actual issue but I thought it would be a nice place to start looking.