So far, we were dropping non-blocking calls whenever sending them would
block. In case a client is sending lots of stream calls (which are not
supposed to generate any reply), the assumption that having other calls
in a queue is sufficient to get a reply from the server doesn't work. I
tried to fix this in b1e374a7 but
failed and reverted that commit.

With this patch, non-blocking calls are never dropped (unless the
connection is being closed) and will always be sent.