I don't suppose you have tried baiting this sucker in have you? The fella I trapped with in Maine said that sometimes the feedbed sours later in the winter and the beaver will be suckered into baited sets like a moth to a flame. One technique he used was to take some wire ties (the zip kind) and strap some poplar twigs to each lower jaw away from the trigger and then submerge the traps on a pole under the ice. He had a picture with a double on one pole (2 traps). He had also said that a thin chunk of PVC strapped to one of the jaws was good for eye appeal.

Although if he is "square shy" I don't know if that would make any difference or not?