SysLogHandler closes tcp session after first message (also noted in #66006)

Bug report

Python 3.10.5
While running FastAPI (Uvicorn) and the SysLogHandler. The Socket if using a TCP stream is being closed after the first message, causing all additional messages to fail stating OSError10083. In looking through the SysLogHandler code I was able to add a try/except that solved the issue by opening a new socket if the current is found to be closed.

Lines 990/991:

else:
    self.socket.sendall(msg)

I changed to:

else:
    try:
        self.socket.sendall(msg)
    except OSError:
        with socket.create_connection(self.address) as s:
            s.sendall(msg)

Your environment

Python 3.10

• CPython versions tested on: 3.10
• Operating system and architecture: Windows 10

从 SysLogHandler 约第 990-991 行附近的 TCP 发送分支开始，使用 FastAPI 和 Uvicorn 在 Windows 10 上通过 Python 3.10 重现该故障。验证 TCP socket 关闭后发送多条消息不会失败；如果仓库中有相关的测试位置，则为重新连接行为添加或更新覆盖率。