Exact answer to question: Eventlet built-in WSGI does not support multiple processes.
Approach to get the best solution for described problem: share one file that contains absolute minimum code required to reproduce problem. Maybe here https://github.com/eventlet/eventlet/issues or any other way you prefer.
Way of hope. Random stuff to poke at: eventlet.monkey_patch(), isolate Eventlet and long blocking calls in separate threads or processes.