How big of a hole are you cutting? If you are cutting a hole large enough that a beaver can swim up into it, they will do so, and knock your snares down as they propell themselves around the pole cutting it. I have @26" of ice now and am guessing you may be close to that. I cut a "Slot" in the ice that is roughly the size of a chainsaw bar or slightly larger, and is parallel to the beaver house and about 3' outside of the feedpile. Then I take a bait pole and lower it into the hole until it hits bottom. If the bottom is hard, I pull the pole back up and sharpen the bottom of the pole with a long skinny point, like a pencil. If it is a loon poop soft bottom I leave the pole cut square. I then lower the pole back to the bottom and just let the pole stand on it's own weight. I then reach under the ice and grab the baitpole with my hand so that the top of my hand is against the bottom of the ice. I then lift the pole back out and put a small mark at the top of my hand on the pole with my hatchet, so I know where the bottom of the ice is at.I then put top of my snares about 2" below the mark on the pole(the nail on your spikes).If it is a hard bottom pond, I then put my bottom two snares so that the CENTER of the loops are aproximately 18-20" from the bottom(imagine a beaver sitting on the bottom and chewing on the pole)because that is what they will do if it is a hard bottom. If it is a soft loon poop bottom, I just put two snare about three inches below the bottom of top two snares. I put a "score" on the pole where each snare is closest to the pole.Then I run my safety cable through the bottom two snares loops, and then up through the top two snares. I then lower the pole through the slot until it hits bottom, and then turn the pole 90 degrees so that the Spikes are pointing to and away from the beavers house/lodge/bank den/most likely direction it will approach. What this does is put the snares directly below the bottom of the ice, points the scores to and away from the house (which is a beavers most likely direction of travel as it leaves or approaches a feedpile/cache), and puts the pole in an area where the beaver most often has a run coming out of the house, adjacent to the feedpile/cache (for the Canucks).
The reason for such a long answer is that I am using the exact same snare you have(5/64" Beaver Spikes)and the beaver are pounding popple here right now.I'm guessing you are cutting too large of holes and the beaver are coming into the holes to work the pole and knocking down your snares with their feet.Heres a couple pictures from the same colony I got the triple in two days ago. Picked up two small ones today from the same three poles and the third pole was cut in half with no beaver.
Probably the same answers as I gave DanS. There are only a couple ways I know a beaver can pull a snare loop down tight and not be caught. The beaver swims by your pole with a brushy limb and the limbs pull the snares down completely shut. The beaver catches the snare loop between their body and their front foot and swims away from the pole.The beaver cuts the pole in half and drags the pole around on the stick lined bottom and pulls the snares shut. The beaver catch the snares between their toes as they propell theirselves around the pole and pull the snares completely shut,or have been caught by a front foot and pull the snare off their fron foot with their other foot and pull it completely shut, and doing so quite often pull the spike off the pole or bend the cable slightly. I've had snares pulled down with small tips of limbs in them many times, and have also caught beaver that had limbs pinned against their bodies by the snare, that they were carrying back to the house.
In some ponds/lakes muskrats will knock down alot of snares, while they chew on the baitpoles, but this is easily recognized by the small bite mark patterns, and sometimes I catch a few of them. When the rats are doing this though, the loops are usually just dropped down to about a three inch loop.