The 'half life' of a popular link shared on Twitter is 3 hours

"We can evaluate the persistence of the link by calculating what we’re calling the half life: the amount of time at which this link will receive half of the clicks it will ever receive after it’s reached its peak. For this link the half life was 70 minutes, which captures all the clicks between the grey lines on the graph above.
Let’s look at a second link - East Coast earthquake: 5.8 magnitude epicenter hits Virginia - , this one first shared by the Washington Post on Twitter.
Rate of clicks per minute on “East Coast earthquake: 5.8 magnitude epicenter hits Virginia”
While the exact details of the traffic are a little different, and the scale of the traffic to this link is much larger, we see essentially the same pattern: a fast rise, and a more relaxed drop-off. Noticeably though this link a half life of only 5 minutes: after 5 minutes this link had seen half of the clicks it would ever see.
This link is associated with a very timely event (an earthquake on the US East Coast) as opposed to the previous link (pictures of otters and kittens are clearly interesting all the time). We think that this difference in content drives the difference in dynamics of these two links. However, one alternative theory that comes up again and again is that the dynamics of the link traffic depend on where the link is posted: do links posted on facebook last longer than they do on twitter?
So we looked at the half life of 1,000 popular bitly links and the results were surprisingly similar. The mean half life of a link on twitter is 2.8 hours, on facebook it’s 3.2 hours and via ‘direct’ sources (like email or IM clients) it’s 3.4 hours. So you can expect, on average, an extra 24 minutes of attention if you post on facebook than if you post on twitter."

Source:  Analysis by Bitly, reported on their blog, 6th September 2011