Minor conspiracy theory: Does Lexus/Nexus keep articles or do they link to the news sites? I realize that is a commercial transaction (and licensed arrangement) so it does not share the "fair use" provisions that FR enjoys.
Also, we hear Rush Limbaugh reading excerpts of articles on the air (sometimes obtained from Nexus searches). I wonder if he (or G.Gordon Liddy) have ever been told that they cannot read even an excerpt of an article (or statement from a political site like antiwar.com) on the air. G.G.Liddy uses a segment of each hour of his show to read articles and editorials on the air (with his own commentary); it used to be a full hour of the daily show but he had no guarantee that every market would broadcast "that" hour.
It might be worthwhile to contact Rush, GG Liddy, and other conservative talk radio hosts who excerpt and read full articles on the air without paying the newspapers.
I think you answered your own question. Lexis/Nexis keeps the articles in a database. Their database is huge. I assume they have a license for each newspaper because they sell the end product, "the search," to their customers.
Reading through all 460 plus responses, I wonder if this is partisan left-wing politics, old fashioned big business, or something else.
Some of these newspapers let you look at the old articles for free, but if you want to retrieve an archived one, charge you. It's possible our archiving costs them money in the long run, or will in the future when they switch to a similar system, so they are trying to whack FR out of the game to make more money.
It could also be the left-wing media fighting back against its critics, or sour grapes from complainers in the Left.