Because the site no longer operates, the reviews cease to exist? Of course not. GameRankings.com has over 2,200 reviews listed for gamedaily.com. That's a lot of info to just turn away. Maybe some adjustments need to be made if you cannot link to the actual review, but acting like the review did not happen is pointless. It's data, so let's use it.
What if, in 10 years time, IGN, Gamespot, 1UP, etc are no longer in existence? Just do away with their reviews?
What if we do as you say, and quit using certain sites/publications when they shut down...In EGM's case, we would have used their reviews, then stopped using their reviews, then resumed using their reviews.