Yet Bernanke continues to be the target of public criticism. Many feel that the Fed’s easy-money policies have continued far too long. What should have been a shot of adrenaline has become a long-term narcotic addiction with ill-understood side effects. By punishing savings and encouraging borrowing, the Fed may be setting us up for another financial crisis down the road.

But people are also angry because they feel the Fed contributed to the 2008 crisis by inflating the housing bubble with low interest rates while pursuing regulatory policies that made the financial system less stable. Alan Greenspan’s Fed refused to impose mortgage lending standards, allowed banks to take on more leverage, and blocked regulation of derivatives markets. It effectively repealed Glass-Steagall restrictions on banks entering the securities business long before Congress formally repealed the law.

In that light, thanking the Fed for avoiding another Great Depression is a little like thanking a doctor for successfully removing a malignant tumor after misdiagnosing it and letting it grow for many years.

Bernanke has learned from the Great Depression, but has he learned from the Fed’s more recent errors in deregulation? To be sure, the regulatory culture of the Fed has changed under Bernanke. It has supported stress testing to bolster big banks’ capital cushions. It has proposed (but not finalized) courageous rules to limit risk taking and interconnectedness among large institutions. Yet much is left undone. The 2010 Dodd-Frank financial-reform law gave the Fed a mandate to impose tougher standards on large institutions, but three years later, the Fed has failed to finalize these rules. New capital rules proposed by the Fed for financial conglomerates are weaker than the standards proposed by the two other regulators, the FDIC and the Comptroller of the Currency, for the banks they oversee. The Fed has yet to propose capital surcharges on the largest financial institutions and new “liquidity standards” to make sure these behemoths can access cash quickly in times of financial distress. Similarly, the Fed has talked a good game about setting minimum requirements for unsecured debt that can convert into loss-absorbing equity if a big banks fails, but has yet to move forward.

So why do the rules languish? Relentless lobbying by large financial institutions surely provides part of the answer. Also, some of the Fed’s powerful career staff may be resisting, still clinging to the deregulatory dogma of the Greenspan years. Some initiatives, like the Volcker Rule’s restrictions on speculative trading, have suffered from the need for multiple agencies to sign off. But most of the rules to regulate big institutions belong to the Fed. In any event, the country needs financial stability, not excuses. Ultimately, it is up to the chairman to stand up to the lobbyists, take charge of the staff, and complete needed reforms.

Bernanke is expected to leave at the end of January. If left unfinished, pending initiatives could be watered down or even shelved by a new Fed chairman. The financial crisis notwithstanding, President Obama is currently considering former Treasury Secretary Larry Summers, an unrepentant deregulator during the Clinton years, to lead the Fed.

Bernanke’s legacy on monetary policy has been set, and we’ll need to wait to see if he made the right calls. His legacy on regulatory policy is far from finished, but he can find the Fed’s path to redemption if he completes financial reform before his term is up.

Fortune contributor Sheila Bair is former chair of the FDIC and author of New York Times bestseller Bull by the Horns.

This story is from the September 2, 2013 issue of Fortune.