So I'm mostly BM. But I actually found melee monk to feel a lot more sturdy than a lot of the other melee dps classes.
But there are couple abilities that might make life easier:
Use Fists-of-Fury on cooldown -- its not just great dps but it also stuns most opponents meaning they aren't doing dps to you.
Use Expel Harm instead of Jab whenever you can if you need healing.
Touch of Karma gives you 10 seconds where any damage you take is redirected to your opponent, on a 90 second cooldown.
Touch of Death. Also on 90 second cooldown, but it can dramatically shorten some fights reducing damage taken.
So if you do touch of karma you, followed by firsts of fury when it ends, you end up with taking no damage for the first 14 seconds of combat. And if the next combat you have enough banked chi to use a touch of death as soon as the mobs health is less than yours, that's 2 low damage fights every 90 seconds.
If you find you are hitting 35% health, consider "Zen Sphere" as your tier 2 talent. Its not the best raid DPS talent, but its something you can cast while moving towards a mob that you can put up before you are in combat; and if you hit 35% health it gives you a burst of healing. Similarly, picking up "healing elixirs" and "chi torpedo" can provide additional self healing. "Chi Torpedo" is particularly interesting because if you are getting close to dying, torpedo'ing away twice gives you a chunk of healing, and means the mobs have to run up to you which gives you time for other cooldowns to come up and self healing things (like zen sphere) to tick and maybe for you to hit a self heal ability. Its not a faster kill, but its faster than running back.
And often, instead of eating, you can just cast a few "Surging Mists". Its still a pause, but sometimes its enough.