I don’t know what might be causing this problem but reisntalling the binding will not require changing anything else.
The fact that everything else with this binding works though points to the binding not being the problem. So the next thing is to recreate the Thing. But that too does not require you to change anything else so long as you use the same ID for the new Thing as the old one. Even the links to your Items will still work unchanged.
But even if you didn’t set the Thing ID to be the same, all you would have to change is the Thing ID referenced in your rules which should be just a simple find and replace.
As always, take a backup prior to making any changes.