Tweets have such a short shelf life that it is worth posting a few times for really great content, to make sure you reach the maximum audience. To avoid annoying your followers, try:
- Posting at different times, on different days to reach people via their behaviour (ie some people will always check twitter over breakfast, others when they're bored in the afternoon. We tend to be people of habit. Consider time zones if you have an international audience).
- Look at your content and think of a new angle for it. Try writing 3 different titles for it, for example - and then each of those headlines essentially becomes its own tweet.
- Use different types of media - try one text-only tweet, one image-only tweet, one combination of the two.