As best I can tell from the error payload in my developer console, Dropbox is actively disabling my webhook endpoint for returning a 202 Accepted in response to the incoming "notification request".
**Update**
It looks like I misinterpreted the documentation that states any "non-200" code will be treated as an error to mean any "non-2xx" code will be treated as an error. I will stand by the fact that it seems odd that a 202 is handled as an error here as it feels like the right response, but I can update our code to return a 200 instead.