This error could be caused by something that affects everyone or something that affects only you. There's a sticky thread under 'connections issues' that shows this error has been around for more than a decade.

This error could be because your mirc is not able to obtain the ip address belonging to the server name. Assuming your problem is not caused because you are trying to connect to something besides twitch, it's a very small chance that twitch is down and everyone has this problem. Sometimes the server name randomly gives you to a variety of that network's servers because they try to balance the load. Sometimes 1 or more of those servers have problems, and you have to wait until their server tries with one that works.

Sometimes there's a problem with your computer's dns cache, where it thinks it already has the correct ip address but really doesn't, causing it to fail. A problem like that often affects other websites not just twitch. If your dns cache is corrupted, this command will clear it, forcing it to get everything again:

/run cmd /k ipconfig /flushdns

Another possibility is that the external dns server you're using has problems.

Here are a couple ip addresses I see from trying to connect to which are not guaranteed to work in the future if twitch changes their hosting, you could try adding these server "names" to your twitch group of your servers list. I obtained these numbers from doing this command inside mirc: /dns