Guys,
The device as at the end of the wires and that is the only place I can change. The contacts at the business end of the wires are 2 mm round, like nailheads. The rolling object is just a chunk of metal moving by inertia. No power of any kind there. I cannot do anything on the contacts end of the wires.
I brought the wires into the shop, so it's a complete device, including actual wires, that works continuously on the bench for 48 hours, but freezes in actual use in no longer than 30 min to maybe 2 hours. went back-and forth between the shop and actual floor several times, and consistently got the same result. The device is LiPo battery powered with 3.3 V buck regulator, so no mains connection - the only thing from the device to the outside world is 6 long wires, that are never connected to anything, except sometimes to each other, but the device freezes even when the wire ends are idle.
Last night I followed GMike's advice and installed 33 Ohm inline, 150 pF behind it to ground, on each of the four analog inputs. Still fine on the bench, I'll have it in actual use for 3 hours this afternoon.