I've had a third-party turbo controller do this on the ps2, which was a shame since I liked how that particular controller felt in my hands better than the default controller.
More recently, my Logitech controller will sometimes do this when playing a game on my laptop, though I'm unsure how much of that is the controller itself versus the computer being dumb. I will be playing fine, a disconnect and reconnect sound will play, and some of the time the character I am controlling will move slow, typically toward the screen. That is when I unplug the controller and plug it back in; then things return to normal until the next time the disconnect sound happens.
Alternatively, on games where I can save manually, the issue just stops on its own, without need to manually reset the connection, for a good while after the save is complete. Compare to something like FFXIV where I have to keep an eye on my character when the USB connection sounds begin, because I cannot save manually there and that controller drift can lead to my character walking off a ledge or into some deadly hazard.
And yet? This never seems to happen when my controller is just sitting idle somewhere; only when it is in my hands. So, again, I'm unsure how much of it is something in the controller's wiring, or how much is the computer looking at the 0s and 1s and proceeding to see apple pancakes until the code it is handling is reset.