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

Comienza en la rama de envío TCP de SysLogHandler alrededor de las líneas 990-991 y reproduce el fallo con Python 3.10 en Windows 10 usando FastAPI y Uvicorn. Verifica que el envío de varios mensajes no falle después de cerrar el socket TCP, y añade o actualiza la cobertura para el comportamiento de reconexión si el repositorio tiene una ubicación de pruebas relevante.