Unfortunately 10053 is just a generic winsock connection error, so it becomes very difficult to track down.
Some of the things that can help:
* Connect via SSL (use ports +6697 or +7000 or whatever for that particular server -- you must include the plus symbol before the port number to indicate SSL). This can stop network hardware or ISPs from disconnecting plain-text TCP sessions that it believes should be terminated or timed-out.
* Connect via hard wire, and not wirelessly. Use an ethernet cable instead of WiFi. Use Cable/DSL instead of wireless services.
* Open up your network adapters and delete the network adapter, then reboot Windows. This is called refreshing your network stack. A new one will be created again and clear out some dead wood.
* Disable or uninstall your nonsense antivirus / internet security software. Use virustotal.com instead when you download files.
* Replace your network router / switch.
* Don't use Bittorrent. You're exceeding the number of TCP sessions allowed by your OS and network hardware.
... and others I'm sure. But those are common ones.