That cat5 crap is their way of saying "we don't want to work on finding a fix so we're only supporting our exact specs even though it will work fine with anything else".
Does it matter which 3 of 4 are used, any combination of 4 will drop the connection? I mean could it maybe be the same 4th you are adding that is causing the issue? Lets say A,B,C work, you add D and it drops. Does A,B,D work? And if you add C to the mix it drops? Could be something in the wiring to the jacks maybe? Try different cables? Or maybe by-pass the internal wiring and try a long cable right from the POS to the switch?