client: Don't make EPIPE fatal if triggered when flushing

If flushing hits EPIPE it should not make it a fatal error since it
would make it impossible to process the rest of the data available in
the buffer. Instead, let reading the socket make EPIPE fatal, letting
the client have the possibility to process the last messages including
any error causing the termination.

Signed-off-by: Jonas Ådahl <jadahl@gmail.com>
Reviewed-by: Daniel Stone <daniels@collabora.com>