Also at play, Washington insiders say, is the sometimes-tense relationship between Petraeus and the White House's national security brass, including President Obama.
"He and the Obama team really got off to a bad start [in 2009] with the run up to increasing troops in Afghanistan," says Korb, referring to a disagreement that became public between the then-commander and the White House over how many additional U.S. troops were needed.
"A few years later, he wanted to stay part of the action," Korb says. "He wanted to be Joint Chiefs chairman, but that wasn't going to happen. But to stay as CIA director, you have to agree that you won't speak out."
When Petraeus speaks to media members, or gives public remarks, these days he generally "talks in broad-brush strokes, not in the much more detailed informative interviews he did in uniform," says Boylan. "There is simply no easy way to talk in an unclassified manner about what the CIA does."
Petraeus has remained mostly silent as several major national security milestones have passed since October, including the first anniversary of the U.S. commando raid that killed al Qaeda leader Osama bin Laden just this month, nor the senior official dispatched by the White House to talk about a foiled al Qaeda plot to use an underwear bomb to blow up an airliner.
Corker says marking such milestones is a presidential task, and Petraeus was right to focus on running the nation's main intelligence-gathering outfit.
"I would have found it odd if he had spoken out about the anniversary," Boylan says. "That's really White House-level stuff."
John T. Bennett covers national security and foreign policy for U.S. News & World Report via the DOTMIL blog. You can contact him at firstname.lastname@example.org or follow him on Twitter.