If your LiveAgent failed to read tweets with message Rate limit exceeded, it means that Twitter rejected 3 consecutive attempts to access its API under your Twitter account (approx. 15 minutes without an update). Chances are, that this error is caused by exhausting your hourly API request limit. read more
Sending data to Twitter (posting), such as posting an update or a direct message, favoriting a tweet, unfollowing or following a user, does not count towards the limit and you can continue to do so even when your rate limit has been exceeded. read more