Oscillator stops when touching with a wire

[mister_e]

Pull-up or pull-down resistor is an easy to test Solution?

[Ron Marcus]

It sounds like static electricity is the culprit here. I understand touching an input, but the ground should be somewhat immune to the phenomena. It sounds like there is a ground loop in the connections. Look for multiple lines connected to ground in the same run of cable. Touching one will cause an imbalance. So if the shield is connected to ground, and another line in the cable is, this could cause a problem. The simplest fix is to not connect the shield on one end of the cable. While it sounds counter intuitive, it might be the cause, or one of them.
Ron