How long it takes a protection is stripped off the car with dishwasher soap depends of course on more things - durability (of whats left of it) of the protection, how much soap is used per wash and how often the car is washed with it.
Btw, if there is not much soap used i think the soap of a coin (self service) carwash is stripping an LSP quicker than a hand-wash with dishwasher soap. The car soap used at a carwash is more aggressive because people want a clean car in a few minutes.
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The video put me in mind of a friend of ours who cleans her Mercedes convertible with Fairy Liquid every week without fail. I must admit it always looks better than you would think!
If there is no protection, then there is of course nothing to strip. A clean car always looks better than a dirty one, but if she would wash her car with a car soap with wax it would look even better.
And i am not convinced with dish washer soap for a car since one of our neighbours use it every other week on his car - the car looks great when wet, but as soon as it is dry the car is dull oxidized.