Some things to try:
- Restart the game
- Log in / out of your twitch account
- Make very sure you're typing your twitch username correctly
- Make sure the browser that opens the page to retrieve you auth token is the same as the one you just logged in with
What firewall / anti virus / operating system are you currently using?
Can you successfully connect directly to Twitch's IRC? Instructions here (can use e.g. mIRC if you are on Windows): https://help.twitch.tv/customer/portal/articles/13...
We're going to fix the infinite spinner on connection failure but would be good to figure out why you're consistently getting a connection failure.