It could be people taking your missing traps, but like some of the others posting i'm more concerned about your staking methods. A 'stick ' may not hold a coon or other animal. Look into getting some re-bar stakes or at the very least wire off to something solid like a small tree or exposed root system.
As far as not catching anything try using some sort of bait such as piece of apple. Muskrats love those.
You have the right idea setting up on sign and trails going in & out of the water. Your traps should be level with stream bed & a bit under the water.
Also, are you offsetting your traps to one side or the other to catch a foot & not in center of a trail to catch chest hair resulting in an empty fired trap?
It's meant to be a joke, but remember an animals legs are on the sides of it's body not in the center of it's chest
There are good books out there, and videos on youtube, on muskrat trapping. Welcome to trapping !