Is there a limit to how many times a US citizen can enter Thailand in a year under the visa-exemption scheme?

There is no official limit to the number of times a US citizen can enter Thailand under the visa-exemption scheme by air within a calendar year. However, Thai immigration authorities may review your entry history to ensure you are not attempting to live in Thailand rather than visiting as a tourist. As long as your visits appear to be for tourism and your previous stay was not overly long, you should be fine.