asyncio prompt example hangs

The following example, taken straight from the documentation (with the first and last line added) hangs for me using Python 3.7.2. I have to kill the process to escape:

import asyncio

from prompt_toolkit import prompt
from prompt_toolkit.eventloop.defaults import use_asyncio_event_loop
from prompt_toolkit.patch_stdout import patch_stdout

# Tell prompt_toolkit to use the asyncio event loop.
use_asyncio_event_loop()


async def my_coroutine():
    while True:
        with patch_stdout():
            result = await prompt('Say something: ', async_=True)
        print('You said: %s' % result)


asyncio.run(my_coroutine())

Can anyone suggest a version that works? I am hoping to make a really simple command-line GUI that uses asyncio and takes input in one panel and prints output in another, but this is a show stopper.

Start by reproducing the documentation example under Python 3.7.2, focusing on the asyncio event-loop setup, patch_stdout context, and async prompt call shown in the issue. Compare the documented example with a working asyncio prompt flow; done means the loop accepts input and prints each response without hanging.