Hi,
It seems like AppVeyor is stable again, and test_asyncio has been fixed, so I suggest to make AppVeyor required again on 2.7, 3.6, 3.7 and master branches.
I just closed the issue of the most annoying test_asyncio failure, test_start_tls_server_1(): https://bugs.python.org/issue33694
Note: There are still two known test_asyncio random failures, but they seem to be rare.
* https://bugs.python.org/issue31007 : test_pipe_handle * https://bugs.python.org/issue33531 : test_stdin_broken_pipe
Victor