Link decay sounds like a new concept to most webmasters, but in fact it's an old one, and has been part of the Page Rank algorithm for a long time now. The easiest way to explain so anyone can understand is that the number of links you have is reducing with passing time, or losing value. But it's not as simple as that!
In some cases you can have 1000 links on Monday, but next week you have only 700, so what happened? You lost the links, they were devalued, de-indexed, content changed, links removed, no-followed, domain expired, got pushed because there were too many links on the page, your bought links expired and you didn't renew? Any of these can be the reason, which is why link building can be a never ending process if you don't go for the quality ones that will last for years to come, and that is not easy at all!
My Personal Take
The main issue at the moment in my humble opinion (along with everything mentioned above) is Google algo, freshness update, query deserves freshness! Yeah, sticking to news trends is great and all, but those links and mentions fade away real soon because they will rely only on a link spike, just like most viral spikes do. On the other hand, high quality content, evergreen content, like tutorials and studies will be there for years and can attract links for years to come if you keep them up to date.
So my personal take is that our content is partially responsible for the link decay effect. Not always, but for anyone relying on white hat SEO and sanctioned link building practices, the type of content can be crucial for link decay effect.
Another thing, I don't believe in the magical power of aged links or links from aged pages! The page where the link is either has authority from the domain, the author, the amazing quality of the content, the number of links and relevance or it doesn't. I don't believe that a link 5 years old can top any link I created two days ago with those properties!
Don't get me wrong on the last statement! Some links do get better with time, sort of! The reason they get better is that the site gets better, the author gains more authority, the page gathers more links, mentions, the quality of the content makes people and search engines recognize the quality. Those things can take time, and thus the links will get better with time, but it's not a simple matter of aging!
Things To Consider
Enough of the theories and personal opinions, you people need advice, and I've got a few when it comes to link decay. Some of them can be found in the upper part of this post, the rest is here:
1. Some links need support - some links will never get indexed, or the pages will be dropped out of index if they don't have links pointing to them.
2. News and hot topics are not constant link generators - unless you are a news site this link tactic is never good in the long run
3. Check for broken links - inner links, outgoing links and incoming links
4. Check your internal and external links - some of your pages may be broken, pages you linked out to may have changed so some links should be updated or removed
5. Consolidate links you build to quality pages - you have your preferred landing pages, link to them, don't get stuck on your homepage and don't link aimlessly as well
6. Check for the number of outbound links - your links may have lost their value (like directory links) because too many outbound links have been added to the page, so keep track of your backlinks
7. Bad neighbors - bad anchors and links to bad sites may lead to your link being devalued, remove it if necessary or ask the webmaster to remove the bad ones, it's hurting him as well
8. Quality decay - some website and blogs tend to be forgotten, numerous reasons, so check if the value of your links and the website where they are starts declining, remove the link if necessary (no link is better than a bad link, which can be said for point #7)
9. Avoid exact anchors - too many will hurt you, some may be devalued, too many will get you penalized
Links will decay, no matter what you do you will lose some links, so gain some more by investing in great content and some outreach. Build content that will always attract links and create a few of your own, but invest in the long run, look for links that will be there for a few years because they offer value, and not some quick link building spam run that will cause a ton of trouble in the end.