How come some links die out and the file sharing website removes the content?

How come this happens?

Well, in the case of Rapidshare, for free accounts the links are deleted automatically after 30 days of inactivity. Links can be removed if someone reports them, or the poster themselves might remove the link for any number of reasons. Bottom line is "grab it while it’s hot".

They do it so they don’t get sued.

Possibly, but the main reason is what Amanda already stated. Free online storage sites like Rapidshare and the now defunct Megaupload remove files after 30 days of inactivity to save bandwidth, regardless of whether that file is illegal or not. And of course, it’s completely up to the uploader how long the file will be available for download. Some only have files available for a very short time, others keep it active for as long as possible.

Also, despite what some people may think, reporting a defunct file link to an admin or moderator will not magically cause the link to become active again either.