It’s true. Links can get old. What you linked to yesterday can be gone sometime in the near future. That is because most all websites and their pages are constantly changing. For your link to be valid it has to go where you intended.
My advice that I give clients who want to link to press resources is that they get a copy for their own use. For example, if you are starting a collection of links to television spots, you can’t be guaranteed that those links will always be valid. In this case they should be trying to obtain their own digital video copy so that they can host the video themselves. The same with magazine and newspaper articles. Ask for tear sheets or try to obtain a digital copy preferably in PDF form.
For links that just go to a website, try to avoid linking to a specific page. Just the web address should be enough. Domains usually don’t change.