You eat alot of salad. And drink alot of water. And eat alot of fruit........

I remember hearing someone say that if you put something large enough above you, you will sleep without losing health.

Everyone has this issue, I tried spawning the iron prop "BedFrame" Sadly, there was no instruction on how to make a mattress. So I still get badly damaged by sleep :C

After having a first damaging sleep a message appeared saying something like "I guess next time I should find a shelter". I right-click-fixed a broad wooden plank on a rock with the phys-gun and slept under it, and it did no damage.
It turns out you must have something solid above your head to stop losing HP while sleeping. Hope that was helpful. :3

Yes, you need any prop directly above you while you sleep in order not to lose health. And you can build a bed to stand on while you sleep to sleep twice as fast as you would without it. I will write a tutorial on Steam Guides today or tomorrow.