I've played a couple low-level monks. I think the trick to survival is to realize that they're not really tanks. As in, don't just rush in at the earliest opportunity and draw the immediate ire of a horde of enemies. I've seen sooooo many monks go down that way. They seem to function better at mopping up once the main party tank has managed to engage the main force of the enemy in melee. Alternate with ranged attacks if this hasn't happened yet or you should be low on health. Unless you can position yourself so that only a few of the enemy can reach you. Yes this will decrease your damage output; sometimes survival is better. Monks seem to work particularly well with battlefield control assistance from allies.
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If they are just jumping in and maxing out damage then they should expect to get knocked down a lot especially if they are jumping into melee first instead of waiting on the tanks. It sounds like this Monk you describe is trying to be a tank when he isn't equipped to be. In doing so they aren't maximizing the Monk's abilities. Maybe instead of using the bonus action for flurry of blows until all ki is spent, this monk could mix in a bonus action to dodge or disengage every now and then?In my experience, they don't. Simply said, they don't tend to survive. The monk in our group is very much DPS and is often tied for how quickly he's knocked unconscious (tied with the rogue). On the other hand, we have two tanks (one of which is my own Fighter/Bard) who can waddle through (thanks to heavy armor) the ranks of the enemy and perform minor healing to get them back from the brink of death. Our other tank is a paladin. We started at level 1 and have made our way up to level 6 so far in the Horde of the Dragon Queen campaign. There were a few close calls, but no one had died permanently...yet.