Well there are a few things to look at. First you mentioned the cables, I would recommend that you use straps over the cables. The cables can slip causing an offset of the snare wires, even very minor slack on one side or the other can drive one mad. The use of straps keeps even tension across the snare wire band, so even if it loosens, the entire set of wires loosen and give a buzz that lets you know.
Second, the activation arm may be too worn to hold the tension. To check this, release the snare (lower the arm to lowest possible position) and use the adjusting knob to raise the strainer body to it's top position (usually turn it clockwise will raise the strainer body). As you lift the strainer arm to activate the snares, there should be alot more tension and the arm should snap/lock in place at the top and hold the tension, if not, the arm will want to fll back down under the tension, meaning it is worn.
Try these out first to see where the strainer stands. Find the right amount of tension on the strainer and wires may take a little time to find the sweet spot for that particular strainer. If changing to straps and making tension adjustments don't do the trick, let me know, there may be another remedy for your problem.