I changed my paddle shifter for downshifts due to a winter jacket accident... Jacket got snagged in the paddle and ripped it off.
On the attached picture you can see how the circuit board looks like. I doubt your problem lies on that end.
Unfortunately I never snapped a picture of the inside of the actual paddle, where there is some plastic that does the actuating on that switch you can see on the circuit board.
It could be that the plastic piece has gotten damaged or even broken off.
I´d open it up and see how it looks, but I doubt there is much to do other than switching the paddle or the circuit board depending on what has given...
Now if it´s loose and floppy, you could be lucky with just opening the steeringwheel up and tightening the screws holding the paddle, but with the paddle loose you´d normally be hearing an irritating vibrating noise coming from the paddle when you are driving your car.