Having the same problem. This is what the log says after the random closing happens.
System.Net.WebException: Unable to connect to the remote server ---> System.Net.Sockets.SocketException: A connection attempt failed because the connected party did not properly respond after a period of time, or established connection failed because connected host has failed to respond 188.165.224.162:80
at System.Net.Sockets.Socket.DoConnect(EndPoint endPointSnapshot, SocketAddress socketAddress)
at System.Net.ServicePoint.ConnectSocketInternal(Boolean connectFailure, Socket s4, Socket s6, Socket& socket, IPAddress& address, ConnectSocketState state, IAsyncResult asyncResult, Exception& exception)
--- End of inner exception stack trace ---
at System.Net.WebClient.DownloadDataInternal(Uri address, WebRequest& request)
at System.Net.WebClient.DownloadString(Uri address)
at System.Net.WebClient.DownloadString(String address)
at Demonbuddy.MainWindow.CheckForUpdate()
Actually not sure if it's the same problem. But yeah...