The issue isn’t the messages your bot is sending, it’s the messages Twitch is trying to send to your bot on that single connection.
This is why you may experience inconsistent results, as at times of low chat activity you may be able to connect to lots of channels, but then at times of high chat activity you will experience issues if that single connection can’t keep up with the messages being sent by Twitch and the buffer builds up to the point where Twitch kills the connection.
The answer to this is to do as Barry suggested, and use multiple connections and to split the channels your bot is joining over those connections, as trying to run 2000 channels on a single connection is excessive.