Sounds to me like you don't have a trigger setup and a spring pole is needed.
Your current set up would be dependent on the animal slipping its head into the noose of the snare and then pulling it tight to strangle itself, not particularly efficient since the critter is going to feel that noose and back out or just hop right through without touching it enough to get hung up.
The best snares incorporate both a trigger mechanism (a figure 4 is very common, easy to build and very sensitive) and the spring pole makes sure the noose closes on the animal quickly as well as jerking it up off the ground.
here are some links to show you how to build them.
offgrid survival
outdoor survival
make a snare