The RICO Act was a huge part of their decline. Tougher drug sentencing as well. Once prison sentences became too unbearable, members became much more willing to inform on other members. Once the code of silence was broken, it became much easier to prosecute individuals, and organizations as a whole, under the RICO Act.
As far as cultural/economic factors, I'm not sure, but there have been several changes in the way the government goes after organized crime, starting in the 1970's, that have made life very difficult for the mafia, legally speaking. Due to these changes, a mobster today is far more likely to be arrested and face prison than they would have been in the early 20th century. These changes can be summarized as: more powerful legal tools to prosecute organized crime, better evidence collection techniques, and a system to protect cooperating witnesses.
First and foremost is the Racketeer Influenced and Corrupt Organizations (RICO) act, passed in 1970, which allows prosecutors to charge organized crime leaders with being part of a criminal racketeering organization, and impose multi-decade sentences for crimes committed by that organization. This gave prosecutors a powerful new weapon with which to go after mafia leaders. Prior to RICO, it was difficult to pin mob leaders directly, as the government had to demonstrate a direct link between those who committed the crimes and those who ordered them. Not an easy task in the days before wiretaps and the witness protection program.
Another development was the rise of undercover detective work, pioneered by Joe Pistone, better known by his undercover name Donnie Brasco. In the late 1970's he infiltrated the Bonnano crime family and was able to gather a trove of information about the inner workings of the mob. Prior to Brasco, undercover work was not widely practiced by the FBI- J Edgar Hoover saw it as beneath the dignity of a federal officer. The effectiveness of Pistone changed that attitude, and in the decades that followed informants became widely used to great effect. A related and equally important development was the increasing use of clandestine wiretaps and bugs to record conversations. This new technology would provide direct incriminating evidence in numerous cases against mob leaders.
Finally, a third major new weapon in the government's hand was the creation of the federal witness protection program in 1970. This had the powerful effect of allowing the government to effectively guarantee the safety of cooperating witnesses, making their decision to cooperate considerably easier.
The cumulative effect of all this was that the government became much more effective in prosecuting mafiosos. The ability to threaten members with long prison sentences, combined with the ability to protect witnesses from violent retribution, made it much easier to turn people state's witness. Once mob leaders are violating omerta left and right, the whole system that made organized crime powerful starts to break down, backstabbing and power struggles become commonplace, and it devolves into something that looks like an ordinary street gang.
The legal changes came in the early 1970's, but it took time for the government to learn how to effectively use the new tools. One of the pioneers in the area was Rudolph Giuliani, who made his name in the Mafia commission trial of 1985. In this landmark trial the heads of the five families were all imprisoned, a coup that would have been unthinkable a decade before. This decapitation signaled the end of organized crime's glory days. It was not fully destroyed and probably never will be, but so far it remains a shadow of what it was in the early 20th century.
I think that along with law enforcement intervention another underlooked cause of the decline of the LCN is attrition due to lack of recruitment.
If we assume that poverty and lack of legitimate oppourtunity breed criminality, we can also assume that the gentrification of Italian-American neighborhoods is partly to blame. It itself a product of the wider assimilation of Italian-Americans into mainstream "White culture."
The same thing happened to the Irish-Americans and the Irish Mob. Without a distinct ethnic identity many belonging to these groups tend to accept legitimate oppourtunities if afforded to them. Each major immigrant group that has arrived to American disenfranchised and destute has brought with them their own segment of organized crime. The Italians were just the most prolific.
So if we consider that there are no more true Italian neighborhoods that breed this culture of criminality where one can get ahead in America by joining the criminal subculture, then it's easy to see why the individual LCN families can never really replinish their member base, let alone grow in any significance.
The LCN is doomed to share the fate of the ethnic crime groups before it. Slowly fade away into obscurity and novelty in the face of the hordes of competing criminal cultures of the newly arrived immigrants. It's an eventuality.
Can anyone recommend a book on various ethnic crime organizations (Cosa Nostra, Russian Mafia, etc...) that have had footholds in the US? I've read several on the Cosa Nostra, but I'd be interested in somewhat of a "survey course" of organized crime in the US.
Secondary question: How much of it can be attributed to the RICO statute? (Not sure if that was the name of the act or not.)