Just to add, I have exactly the same problem.
Looking at the sensors, one of them has rough paint so I'm guessing it's corroded under the paint. I'm going to lightly sand the paint back and see if I can remove any of the corrosion.
Does the beeping sound come though the cars speakers? I'm changing to an aftermarket head unit shortly, so I'm hoping that will stop the constant beeping when I'm in reverse?