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I am curious why you are asking. What have you heard?
No, they don't.
Most extended warranties are not worth the paper they are written on. Were the manufacturer lets lots of stuff slide by the warranty companies will not and most repairs after a couple of years are created by the consumer. If you do decide to do it make sure it is a warranty company and not through the selling dealer. That way if the dealer goes out of business you might still get some coverage.
Well, You could trade it in every 5 years when the warranty runs out for a newer model with a brand new warranty.
A good spa should last 12, 14, 16+ years whether you keep it that entire time or pass it along. Buy it with the idea you'll at least keep it 8 years before trading in or selling and getting another.Beware of any lifetime warranties. There is almost always a catch with anything that says "lifetime".