Hide, is the button hard or do you have to push it hard for it to work? The problem will probably alleviate a bit if you clean it with alcohol, both the pad and the board contacts... I am not familiar with your caller but the pad seems similar to what the computer keyboards look inside. Might be worth a shot if you are comfortable taking it apart. At lease it might give you more time to shoot and then you can send it to the manufacturer when season i slow...
You guys lucky, there is not such thing as calling a coyote here in the thick SE....