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. E.g. if you use a Twitter client on a smartphone, tablet and a computer, this scenario is very probable. Unfortunately, there is no way for us to download your tweets, if other applications deplete the rate limit for your Twitter account. However you can:
increase the auto-reload intervals on other clients, e.g. 15 minutes.
unregister all unused applications and services connected to your Twitter account
wait and hope that some of our requests do eventually get through :)