Fix swallowing exceptions and explicitly cap retries in process_response

[albertyw]

This PR rewrites the retry logic in process_response to not use break in finally (#745) and to put an explicit cap of 2 attempts to process a response before letting the request continue on through the middleware.

The original code also implicitly had a cap of 2 attempts because finally: break would have executed regardless of if _process_response succeeded which meant there would always be either 1 attempt (try) or 2 attempts (try and except), never any more. The original likely meant to have else: break to retry forever, but retrying forever is likely undesirable in this situation.

Follows up on #140
Fixes #745