Agreed, it almost has to be a connection issue or faulty stepper drivers. There is also a chance that another program on your computer could be sending random stuff over the line connected to your machine.
Vicious had the right idea to switch axis and driver combinations. X and Y would probably be the easiest to see the problem. If you plug the x axis into the y driver and the y axis into the x driver you will pretty quickly figure out where the issue lies.
He also had the right idea with checking continuity through each wire while moving it (machine powered off and motors unplugged). I have wasted many hours troubleshooting problems by assuming that wires with no visible damage are fine. If you don’t already have one, a multimeter with a continuity testing function is worth every penny.