Are remotes on ceiling fans a serious repair problem?

They can be a pain and tend to fail more than a normal wall switch or pull chain. The receiver is usually in the canopy and the hand held remote something's disappears when you need it repair is usually not possible unles it is something simple like a moved dip switch. Replacement of both units is the norm.

Yes they are. Quality control for them is pretty much nonexistant so they fail Consistently. I always advise consumers to buy fans WITHOUT REMOTES.

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