From what I'm guessing here your router has a very small TTL (Time To Live) for NAT (Network Address Translation), too short for the "Check connection time out" to be effective. NAT connections are set up by your router and will eventually be dropped if no data goes forth or back.
Increasing the TTL (if possible) or forwarding the IRC port to your computer specifically might do the trick. Note that if you decide to forward, you need to make sure that your computer and the computer running your bot use different ports.
