I've had the same thing happen to me a couple times, always seemingly on the way to the airport even. It's really frustrating. In those situations, I generally switch to Lyft and get picked up without cancellation. Unfortunately this isn't an option in places Lyft has pulled out of due to regulations like Houston that Lyft has pulled out of due to similar regulations by and thus only Uber remains.

This is one of the unfortunate side effects of a car service pulling out of a city like Lyft did in Houston. Now only Uber remains which, despite its flaws, is light years ahead of the standard yellow cab service.