Seems a little odd, was it coyote hair in the trap? Could you have caught a feral cat or rabbit and was eaten by an owl or hawk. What size trap are you using? What type of sets do you have in? A dirt hole set has the hole behind the trap, the coyote needs to step in the trap to see/smell the hole. Traps are clean and aged, I'd hang my cleaned and waxed traps in a tree/under the eve of the trap shed for quite awhile before the season starts. Fresh bait in cold temps give off very little scent.
How much trapping experience do you have? Past success on coon and mink on dry land.
Three days is a short time.
