The "Tasini Decision" refers to the US Supreme Court case NEW YORK TIMES COMPANY, INC., ET AL. v. JONATHAN TASINI, ET AL. (533 U.S. 483). The decision states: "Reproduction of freelance authors' magazine and newspaper articles in computer databases, without authors' permission, held to infringe authors' copyrights and not to be privileged under 17 USCS 201(c)".
Prior to this ruling, many publishers had include all articles that appeared in the printed newspaper or magazine in the electronic versions of these publications including the feeds that they provided to online aggregators such as LexisNexis. The decision meant that authors had to agree to electronic reproduction of their work before it could be used in this way.
The ruling affects the free online version of newspapers on the open Web as well as subscription-based databases including LexisNexis. When a freelancer chooses to withhold electronic publication rights, the publisher simply omits the article from the feed that is sent to LexisNexis. No notice is provided that the article is missing. Thus users may find that an article they read in print has simply disappeared from the online version of the publication. This is a relatively rare occurence as most freelance articles and all articles written by newspaper or magazine staff are now explicitly licensed for online reproduction.
How to tell if an article is missing
It can often be hard to tell if an article is really missing or if the search you have designed is simply missing it. See the article on Academic Searching: Find All Articles for techniques to list all article from a specific date or date range.
Where to find missing articles
Microfilm archives of newspapers and magazines are not affected, so these are good sources for older articles that have been withheld from online publishing. Many libraries also have archives of the print editions of some newspapers and magazines.
Link to the decision in LexisNexis Academic: 533 U.S. 483
Wikipedia article on New York Times v. Tasini