I’ve had problems with this on 360 Hori sticks as well…
Two of them pretty much died a year and a half ago. One was dropped, the other seemed like it had short out while I plugged it into a system that was already on.
Out of the two sticks I currently have, one of them now requires being plugged in while the machine is off, then turning the machine on. If I plug the controller in while the machine is already running, the green circle flashes and well, nothing else–just keeps flashing. I think this stick was dropped by one of my customers.