But Italian authorities say they have struck a blow against the secret network, with the arrests in Sicily of 11 people they accuse of being Mafia members.
Among them are those with no criminal records and little to suggest a connection with organized crime, including a shepherd, the owner of a dairy farm, a truck driver and a surveyor.
According to police in the Sicilian capital of Palermo and the anti-mafia department, these suspects were part of a "men of honor" structure that since 2012 had allowed Messina Denaro to relay his orders and stay in charge.
They'd meet clandestinely in remote countryside locations to hand over the boss' letters, or "pizzini," using carefully coded language when they spoke to avoid detection, a police statement said.
Bank accounts scrutinized
The pizzini -- little pieces of paper wrapped in tape and destroyed after reading -- were delivered only every three months in a bid to escape the attention of investigators and prevent them tracking the origin of the notes, police said.
Police interceptions revealed that the "postmen" for the boss used a kind of coded farmer's language to conceal their meanings, referring to "sheep to shear," "vegetables to harvest," or "ricotta cheese" that needed to be collected.
The mail exchanges were carried out in open countryside because the noise made police wiretapping more difficult.
But despite such precautions, the net appears to be closing in on Messina Denaro.
Another 18 people were seized as part of the same police operation.
Other financial investigations are underway in Swiss banks regarding bank accounts that investigators suspect have been used to finance Messina Denaro's life on the lam.
At a news conference Monday in Palermo, Procurator Teresa Principato said investigations into Messina Denaro continue and are now focused on finding whoever has been shielding him since he went on the run in 1993.
"It's clear that he has very, very important protections," Principato said. If he wasn't protected at a high level, she added, "it wouldn't be possible for him to be still be a fugitive after so many years" during which the Cosa Nostra's sometimes deadly operations have continued.
Italian columnist and mafia expert Francesco La Licata wrote Tuesday in the national daily La Stampa that Messina Denaro is the last of the Mafia bosses on the run for whom "it's worth the hunt," in terms of the huge "human and economic resources" needed.
Suspects in their 70s
Those arrested include 77-year-old farmer Vito Gondola, who had previous convictions, the police statement said. He's accused of being the Mafia head in the Mazzara del Vallo district and having had a pivotal role in the delivery of Messina Denaro's messages, coordinating times and methods of delivery.
Others detained are 77-year-old Pietro Giambalvo, allegedly a member of the Mafia clan of Santa Ninfa who met with Gondola, and Leonardo Agueci, a 27-year-old accountant with no criminal record who's described by police as a loyal person used to relay communications between bosses.
Police accounts of the notes passed between Messina Denaro and his alleged network may ring a bell with Mafia watchers.
In 2006, investigators swooped on then-Mafia boss Bernardo Provenzano -- on the run since 1963 -- capturing him without a struggle near his Sicilian hometown, the village of Corleone, the same made famous by author Mario Puzo in "The Godfather."
Then aged 73, Provenzano was accused by authorities of having run the Cosa Nostra with an iron fist since taking charge. His modus operandi? Orders passed to underlings through precise, tightly-folded paper notes.
Prime Minister: Let's capture the top boss
The latest moves against those with suspected Mafia connections come amid an apparent determination to crack down on organized crime in Italy.
In a post on his official Facebook page, Italian Prime Minister Matteo Renzi thanked all those involved for "the blow inflicted to the Mafia organization" through the arrests.
"Let's now move on to finally capture the super boss on the run. Italy is here, all together and united, against organized crime," he said.
In March, Italian President Sergio Mattarella told CNN's Christiane Amanpour how his own brother had been murdered
at the hands of the Mafia more than three decades ago.
"In all these years I've always tried to emphasize and to promote the need to combat the Mafia," he said. "Because it is a cancer which is oppressive and which stifles everybody's freedom and reduces the possibility for the areas in which it's present to prosper and to develop."
Speaking in Turin in June, Pope Francis also urged his audience to fight back against organized crime and corruption.
"We say 'no' to corruption that is so widespread that it seems to be an attitude, normal behavior," he said. "But not in words, rather in deeds. We say 'no' to Mafia collusion, fraud, bribes, and the like."