Google's John Mueller said that links do not expire, but it may be the case that links can become less important over time as the pages that link to you become less relevant over time.
John said this at around the 49:43 mark into a video hangout last week when he was asked "Do links expire after a while? I mean the signals that they're passing."
John Mueller immediately said "no, they don't expire." But he added that links can become less important to Google over time as the page that has the link on it goes deeper and deeper into the site that is linking to you. The example he gave is that when CNN links to you, when the link is off the home page, it is more important, but two years later, if that article is somewhere in the CNN archives, that link may become less and less important.
Here is the video embed:
Here is the transcript:
Question: Do links expire after a while? I mean the signals that they're passing.
Answer:: No, No. They don't expire.
What does happen though is that, especially if you're talking about a large website that's growing regularly, then the pages that links are on over time they get like even deeper and deeper within this website.
So for example, if you have a link from CNN and it's in an article that's linked on the homepage, then that's something that's really important for us. On the other hand, if this article is maybe a year or two later, is somewhere in the archive at CNN, then that article itself is not something that we would find that important anymore.
So it's not that the link expires after a certain period of time. But just often that the page where that link is on that becomes less and less relevant over time, if it's on a site that is growing fairly regularly.
Forum discussion at YouTube.