A flapper valve is that valve in your toilet that produces the flush.
But I don't think that's what you ment since you posted your question in the pumps & wells forum.
So another flapper valve is used in oil well construction to prevent a blow out.
Or... do you mean the flapper valve used in water wells to add air to a non-bladder type pressure tank.
Can they go bad, yes anything can go bad, what happens, your water tank gets waterlogged and your pump cycles real fast and burns up.
It's normally on the drop pipe inside the well casing, you pull the pump and pipe up about 10' you should see it.
Rancher