This issue is a known problem with the Subathon Tool. Unfortunately, we've had no success in fixing it. However, one temporary solution is to go to the Countdown tab, and click "Disconnect". This doesn't actually permanently disconnect you from the chat servers. When you click it, it will close any connections to Twitch servers, but will automatically initialise these connections again. It's a reset button! You'll keep your current countdown values, sub values, uptime etc. but will have your connection to chat refreshed. Think of it as a manual refresh on Chrome, you won't lose anything.
Hopefully this works for you (if needed, try clicking it multiple times). As mentioned, we're aware of it, but currently can't find where or why it occurs. It could be Windows or Twitch getting in the way, but it's still being looked into.
Mike,
Lead Developer