Should Sec of Def. Carter reduce GEN Petraeus back to LTG after he has retired?

This Washington Post article describes how Petraeus managed to get off so lightly, and perhaps why he faces losing a star after all:
https://www.washingtonpost.com/world/national-security/how-david-petraeus-avoided-felony-charges-and-possible-prison-time/2016/01/25/d77628dc-bfab-11e5-83d4-42e3bceea902_story.html

I understand that the SecDef has the authority to do this, what I haven't seen is any indication that he has any intention of doing this. What reason do we have to believe this is likely?

I posted a link which explains why this matter has been brought to light now. Take time to listen and you will understand: https://www.rallypoint.com/shared-links/joe-biden-to-the-rescue-1-20-16-monica-crowley

We report to a CIVILIAN boss. They hire and fire us. We serve at their pleasure. Please take a moment to remember all of the countries then (and unfortunately, even now), that practiced military leadership and what inevitably happens to them.

A more juicy aspect is if he's busted down in the near term and the political firestorm. That is possible given the programmed smoke screen announcements and actions that are geared to taking the public's eye off the real issues like ever increasing taxes, less purchasing power, etc. A second aspect besides this short game distraction is the long game. So the Administration flips and both Congress and the Executive are Republican. Will the juices flow enough to restore the rank? Perhaps not. It would be another example of casualty by political whim. Happens all the time.

At what point is your military career over and not effected by mistakes made as a civilian? Once you retire and no longer wear the uniform it should be over. Exception; after you are out a military investigation finds that while you were in the military you committed a crime that violated the UCMJ. You can be prosecuted and punished accordingly and reduced in rank.

All of the good works we accomplish become dust when a conscious decision is made to violate the trust placed in us. Those few seconds of 'stumbling' define our total efforts, regardless of how great they may have been just prior to that moment. The public will only remember the scandal that General David Howell Petraeus became embroiled in...his admittance that he gave classified information to his biographer and mistress while still in uniform. For those of you out there who attempt to protect him or easily dismiss his indiscretions - just how do you believe you would have been treated under UCMJ if you did the same thing? In equal measure to anyone out there, he is protected by due process and innocent until conclusively found to be guilty. There's a significant amount of fact and evidence hidden from the public due to position, security clearance, and rights under the Constitution. Such evidence is available to those with oversight of the General Officers of our military and not made known to the public due to National Security. Ash Carter, the present Secretary of Defense, is reconsidering General Petraeus's transgressions under the idea that even so highly placed a military commander is not immune to accounting for his acts. Five-star General of the Army Douglas Francis MacArthur was fired by President Truman for making public statements on Presidential policy matters. General Kevin P. Byrnes, Commander of the Army Training and Doctrine Command, was relieved of command (fired) for disobeying a lawful order from Army Chief of Staff Peter Schoomaker to break off a consensual relationship with another woman (his divorce proceedings were not yet finalized). The unique irony? I was General Byrnes's Inspector General with the 1st Cavalry Division in Bosnia during the Balkan conflict and could have easily advised him against what he was doing.

If UCMJ is pursued, I hope the court takes all information into account. Just my $0.02s.

Don't know if it is Possible. Last time I checked Congress decides what Rank you retire at for a Flag Officer. As SECDEF he may be able to Petition Congress to Demote him in the Retired Ranks but It would take a bit to see if there is even Precedence for such an action.