The Post Sports Live crew discusses Ray Rice's release from the Baltimore Ravens and his suspension from the NFL after new video surfaced of a domestic violence incident involving the running back and his wife. (Post Sports Live/The Washington Post)

Hour by hour, Roger Goodell’s mission to preserve the game’s integrity is failing, and any further discussion of his inability to properly deal with the NFL’s domestic violence problem has to begin and end with the commissioner’s necessary termination — preferably before Sunday.

It comes down to this: If Goodell’s league cannot better protect battered women, what good is this moral armor Goodell has the audacity to call “The Shield”?

A day after he emphatically said that before Monday, no one in the league offices had seen video of Ray Rice knocking out his then-fiancee in an Atlantic City casino elevator, the Associated Press essentially called Goodell a bald-faced liar.

By launching an independent investigation overseen by two of his closest owner/allies, Goodell’s best hope is to emerge from this unseemly mess looking just horribly naïve and incompetent, rather than duplicitous and phony.

Either way, it’s over. He will never again recapture his popularity or be seen as the credible omnipotent authority he once was as NFL commissioner. When Drew Brees and others have snatched the gavel from Mr. Law and Order and said he must be also held accountable for his actions, it’s only a matter of time.

The White House said Monday that men need to band together to combat the acts of violence perpetrated against woman. This comes in the wake of a new video showing former Baltimore Ravens running back Ray Rice striking his then-fiancée in February in an Atlanta elevator. (AP)

Each day this becomes less about the demonization of Ray Rice and more about Goodell’s derelict of duty.

And the only thing that can save him now is the greed of owners and good, old-fangled fans who don’t give a lick about off-the-field matters as long as their guy is strappin’ up Sunday.

If some of the NFL’s most respected and influential owners — Bob Kraft, the Maras, the Rooneys — have neither the foresight nor courage to fire the man who has exponentially grown their franchise values yet cannot sufficiently stand up for women knocked unconscious by the very players Goodell is paid to discipline, their product should be severely devalued until he is gone.

And if no tangible loss in attendance, viewership or their byproduct revenue is administered, if this is only just feckless social-media outrage in the moment, then the NFL really is bulletproof and will know that, when push comes to knockout punch, Goodell and the owners can always count on the greatest enablers of America’s most powerful sports league: us, the ticket-buying, RedZone-subscribing public.

If we can’t kick our addiction to sanctioned violence for one Sunday to show solidarity for women who deserve much better from a league than simply donning pink for charity each fall, we indirectly participate in the depravity Rice showed when he viciously dropped his then-fiancee in that elevator.

If Goodell remains, greed wins. If no action regarding his removal is taken, our 24/7, ADHD news cycle wins. Above all, if Goodell stalls and stays, apathy wins — the same kind of apathy that makes a league and a team look away as stadiums fill each Sunday.

As Elie Wiesel, the activist who survived three concentration camps, once said: “The opposite of love is not hate, it’s indifference.”

If the Associated Press report from Wednesday is true, the NFL will have shown callous indifference amid its worst public-relations crisis under Goodell. Robert S. Mueller III, former director of the FBI, is now entrusted with getting to the bottom of the sewage. Unfortunately, the other owner overseeing the investigation along with Pittsburgh’s Art Rooney II is New York Giants co-owner John Mara, who has already decided the notion of Goodell stepping down is “misguided.”

As usual, the deck is stacked so that any transgression at the top becomes viewed through the prism of mostly white, wealthy conservatives, who see profit as king and anything that stands in its way a general nuisance.

But after the annual $9 billion in revenue, they can’t get around these numbers. In almost nine years with Goodell as commissioner, 56 players have been arrested on charges of domestic violence, some multiple times. Those players have lost just 13 games combined.

Brandon Marshall accounts for three of those. He was arrested twice, acquitted once and the other charge was eventually dropped. The Bears’ wide receiver just happens to be the only active player on a studio panel show this year, Showtime’s “Inside the NFL.”

A player who has not been suspended yet is Carolina’s Greg Hardy, who was convicted in July of assaulting his former girlfriend and threatening to kill her. The 6-foot-4, 265-pound Hardy dragged her by the hair room to room, the testimony read, before putting his hands around her throat.

“He looked me in my eyes and he told me he was going to kill me,” the victim said during the testimony. “I was so scared I wanted to die. When he loosened his grip slightly, I said, ‘Just do it. Kill me.’ ”

His case under appeal, Hardy played in the opener last week and is expected to play Sunday. Panthers owner Jerry Richardson, another big Goodell supporter, won’t terminate or suspend Hardy, getting as many games out of him as he can in case Hardy loses the appeal and the league has to be punitive for the sake of appearances.

Did we mention Richardson got the Echo Award Against Indifference on Wednesday night in Charlotte, where Goodell was supposed to honor him but pulled out after the AP story basically accused him of indifference.

“The NFL has a violence against women problem,” said Terry O’Neill, the National Organization for Women president who called for Goodell’s ouster on MSNBC Wednesday night. “It’s not a Ray Rice problem. It’s a violence against women problem. You need a real leader who will take on this problem and create new solutions.”

She’s right. Roger Goodell never hit a single woman and has never been charged with domestic violence. But the Lord of Discipline turned out to be a lightweight when it came to the most serious test of his stewardship: using “The Shield” to protect women such as Janay Palmer Rice, whether she thinks her husband did anything wrong or not.

From the league’s efforts to suppress concussion research or to its claims of plausible deniability on the next third-rail topic, Goodell’s lack of transparency on many issues has bolstered the need for his removal. But the Ray Rice episode seals it. It’s not just inexcusable; it’s almost as cowardly as throwing that punch.