The bank's oversight committee -- which consists of 47 of the world's finance ministers and leaders of other organizations -- gave an unusual public rebuke to Wolfowitz's leadership of the organization on April 15, saying it had "great concern" over the organization's future.
However, Wolfowitz told journalists in Washington the same day that he does not intend to resign.
"I believe in the mission of this organization, and I believe that I can carry it out," Wolfowitz said. "I've had many expressions of support."
Some analysts say Wolfowitz could be fired at any moment, while one says the board may plan to embarrass him enough to weaken him and then keep him in his job as the board's puppet.
The oversight committee said in a statement that its concern in the case is to now "ensure the bank can effectively carry out its mandate and maintain its credibility and reputation as well as the motivation of its staff."
The tone of the committee's statement made it clear that the bank's overseers do not consider Wolfowitz's apology of last week sufficient to close the subject.
"I wish I had trusted my original instincts and kept myself out of the negotiations," Wolfowitz told bank staff on April 2. "I made a mistake for which I am sorry."
By any measure, the scandal is a complicated one that the bank cannot easily resolve.
That is because Wolfowitz never made a secret of his relationship with Shaha Riza, who was a communications officer in the Middle East and North Africa bureau of the bank when Wolfowitz came to lead it in 2005.
Wolfowitz told the bank upon his arrival that his relationship represented a conflict of interest, and he offered to remove himself from the process of resolving it. That process was the transfer of Riza outside the organization while remaining on the bank's payroll.
Instead, the bank's Ethics Committee allowed Wolfowitz to take part in arranging a deal that transferred his partner to the U.S. State Department. In the transfer, Riza's salary jumped from $132,660 to $193,590 -- more than the salary given members of the U.S. president's cabinet.
All this makes the scandal not only a question of Wolfowitz's behavior but also of how well the bank's own safeguards work.
And that calls into question the credibility of an institution that regularly presses the countries to stamp out corruption and to be more transparent about how loans they receive are spent.
It is too early now to say how the bank will resolve its crisis. But most analysts agree that almost any option spells serious trouble for Wolfowitz, who even before this crisis faced hostility at the bank.
Brett Schaefer, who studies international economics at the Heritage Foundation, a policy research center in Washington, says some of that hostility comes from Wolfowitz's previous involvement in planning the Iraq war when he served as the deputy to then-Secretary of Defense Donald Rumsfeld
But Wolfowitz's policies at the bank itself also made him some powerful enemies.
Shortly after he became the bank's president, Wolfowitz began a campaign against corruption in some of the countries that receive the bank's loans. His critics, both within the bank and outside it, say Wolfowitz punished these countries too harshly or for the wrong reasons.
In 2005, for example, Wolfowitz refused to approve an aid package for Uzbekistan. This move followed Uzbek President Islam Karimov's decision to stop allowing U.S. military aircraft to use air bases in his country.
Wolfowitz says that he made the decision based Karimov's poor human rights record.
"He's got three different angry constituencies lined up against him," Schaefer says. "This would always be a very difficult and dicey political situation within the bank, but now he's compounded it by making a personal mistake, and that is getting involved in questionable activities with his companion. And so his personal conduct is being used by those who would normally be opposed to him as well. This does not excuse what he may or may not have done in the situation with his companion. But I think it's being exaggerated for other reasons."
What The Future Holds
There are reports around Washington that Wolfowitz is now in varying degrees of trouble with the bank's executive board.
Some say he could be fired at any moment, while one says the board may plan to embarrass him enough to weaken him and then keep him in his job as the board's puppet.
Schaefer says he suspects Wolfowitz's fate won't be so grim. In fact, he predicts the furor over his female companion probably will be forgotten by the summer.
In the meantime, Schaefer says, many people believe the bank needs reform, and reform often means ruffling the feathers of veteran employees.
But he also says that Wolfowitz may have ruffled so many feathers that a second term as World Bank president in 2010 is now a very remote possibility.