If this error often happens to you, what can you do? You can lengthen the interval for automatic refreshes, thereby reducing the number of automated connections per hour. For example, in Twitterific, you can adjust the interval from every 3 minutes to every hour or even never. I currently use "every 10 minutes," and have never had the error message pop up.

By the way, to see these error messages in Twitterific, you need to make sure that the preference to "Show errors in tweet list" is enabled.

Unfortunately, turning off the messages will not prevent the time-out if you exceed the limit. It just turns off the notification.