"non-condensing" in this case is basically where the equipment could be dissipating heat and actually be below the dew point of then surrounding atmosphere. While the atmosphere may be at 99% humidity at the current temperature, if the dew point is very near that temperature, your equipment could actually be cooler than the dew point. In that case, water vapor could be condensing on items/surfaces in that equipment. I'm sure you've seen a glass of ice-water with condensation on the outsides. The room temperature is probably well above the dew point and the humidity level can even be quite low. But that condensation will still ruin an unprotected wood table top...
Many concrete floors that are protected from the Sun (a roof but open to outside air)and in contact with the ground above the frost level (without thermal insulation around the edges), will "sweat." But that doesn't mean that there will be water dripping from the walls or ceiling.
There are two "simple" ways to prevent this:
1. Enclose the equipment in air/water-tight enclosures.
2. Heat the local atmosphere, even if it is only the area near the equipment.
There are several others means of protection, of course:
1. Move to the desert.
2. Heat/condition (dehumidify) the room.
3. Move the equipment into an environment within the specifications humidity range.
BTW, the humidity levels reported by the weather bureau is not the same as the 'non-condensing' humidity level.
I'm not saying this is your problem, but the symptoms sound like humidity problems to me. It could even be that parts of some connections or even the circuit boards have hairline cracks that only affect operations below certain temps that cause things to contract a little.
I do have one suggestion. Next time this happens, have Sneakers take a hair dryer out there and blow some warm air on the equipment...