It sounds like the kiss of death for your driver board. Something is failing when it gets warmed up or put under pressure.
There is no reason why Mach 3 should suddenly stop putting out signals - especially on just one axis.
To test it use two other output pins (if you haven't any spare, swap the x and y, or x and z) and reconfigure Mach 3 to output on these new pins.
If the fault moves (or does not appear) then the trouble lies with the computer side. If the fault stays with the same axis, the fault lies with the driver board.
You can, of course, test this by swapping the driver boards - i.e. inputs from the computer AND outputs to your motors swapped and see if the fault moves.
If you have to replace the driver I would suggest you use a single axis driver card. The trouble with 3 or four in one, with a breakout board is that if something goes wrong you have to replace everything. You could just use a seperate single card, and leave the faulty axis on your main board disconnected. That would get you going.