After years using mIRC with no problems, I began getting this 10053 constantly. It happened with version 6.x or 7.x as soon as I got a D-Link DIR-601 router.

Modifying the following two settings solved the issue. Hope this helps someone.

Router setup page > Advanced > Firewall Settings > NAT Endpoint Filtering. Set both TCP and UDP to "Endpoint Independent".

From the D-Link help:

Endpoint Independent
Once a LAN-side application has created a connection through a specific port, the NAT will forward any incoming connection requests with the same port to the LAN-side application regardless of their origin. This is the least restrictive option, giving the best connectivity and allowing some applications (P2P applications in particular) to behave almost as if they are directly connected to the Internet.