If the server disconnected, all players would be force-quit from the match and there would be nothing to rejoin/reconnect to. Are you seeing the rejoin button? Or are you having problems logging in? These are related but different issues.
While the problem might not be at your house, it could be somewhere in your ISP’s route to the server itself.
These steps may help:
If not, make sure you add your WinMTR here for someone to look over.