Well worth checking the supply voltage, I think. It may be that you're getting enough variation to cause the charger(s) to drop back when they sense a voltage drop. The semi-random nature of the symptoms is odd, and I doubt it's related to the charge point, TBH, as there's nothing within the charge point to throttle back the current, only the charger(s) inside the car are able to do that.
The obvious possibilities (there may be others) seem to be:
1. Location-related charge current setting being the culprit - doesn't seem likely now that the location is showing correctly.
2. A software problem with an app (possibly related to a charge point) signalling to the charger(s) to throttle back. This is possible, but if the charge point is set to dumb mode, and not using any connectivity, then the charger(s) should run at the full current that's being signalled as being available, as long as the setting in the car is at 32 A.
3. A voltage drop or low voltage that's being sensed by the charger(s) as a potential fault condition, causing them to throttle back.
It seems you've eliminated the first, and possibly the second, of these, so that leaves voltage drop as a relatively easy to check thing.