The tests

    test.test_asyncore.TestAPI_UseIPv4Select.test_handle_close_after_conn_broken
    test.test_asyncore.TestAPI_UseIPv6Select.test_handle_close_after_conn_broken

can fail randomly (see python issue #29151 [0]). Sleeping for a short moment
before writing bytes to the socket seems to circumvent this problem.

[0] https://bugs.python.org/issue29151

diff -ur a/Lib/test/test_asyncore.py b/Lib/test/test_asyncore.py
--- a/Lib/test/test_asyncore.py
+++ b/Lib/test/test_asyncore.py
@@ -632,6 +632,7 @@
         class TestClient(BaseClient):
 
             def handle_write(self):
+                time.sleep(0.01) # workaround for issue #11265
                 self.send(data)
 
             def handle_close(self):