My guess is that there is a slight potential difference between the ground signals. A500/A2000/A1200 might be more tolerant for it, while the other machines are not. Also if it's close to the border condition (the issue causing problems or not) it can happen that the problem goes away and reappears by just changing the configuration slightly. This may lead to puzzling results if you try to identify the problem by eliminating or swapping the HW for instance.
Are you using grounded sockets for both the amiga and the monitor? Are the grounds in the same potential (that is: are the plugs connected to the same ground)?
