Three years after he was sent to prison, con man Bernard Madoff continues to haunt the Securities and Exchange Commission.

The agency says it needs a bigger a budget to police the financial world and protect investors. But some members of Congress cite the SEC’s failure to stop Madoff as one in a series of reasons to think twice before trusting the agency with more money.

“I think this body is reticent to throw more money at the SEC until ya’ll have proven that you have addressed the structural problems from within . . . in a comprehensive way,” Rep. Jo Ann Emerson (R-Mo.), chairman of the House appropriations subcommittee that holds the SEC’s purse strings, told SEC Chairman Mary L. Schapiro at a hearing Tuesday.

Emerson opened the hearing on the SEC’s budget request by recounting a litany of problems.

“Since 2001, SEC’s budget has increased over 200 percent,” Emerson said. “Despite this tremendous growth in resources over the past decade, the SEC failed to detect Ponzi schemes such as Madoff and Stanford, the U.S. financial system nearly collapsed, and judges continue to question SEC settlements and regulations.”

“In recent years, the SEC has also had several embarrassing management lapses, such as purchasing unneeded space, destroying investigative documents and repeating material weaknesses in SEC’s own financial statements, to name a few,” Emerson said.

Rep. Jose E. Serrano (D-N.Y.) was more sympathetic to the agency.

“You are responsible for making sure that what happened in the past doesn’t happen again,” he said, as Schapiro waited to testify.

Emerson steered the discussion back to Madoff, who carried out a long-running Ponzi scheme under the noses of SEC inspectors. “It just worries me that in spite of how much money we threw into the SEC, that we still, you all still missed Madoff,” she said, acknowledging that that happened before Schapiro became chairman in 2009.

The SEC is seeking a budget of $1.6 billion for the 2013 fiscal year, which would be an increase of $245 million, or 18.5 percent, over the fiscal 2012 appropriation.

The agency says the money would help it carry out greatly expanded responsibilities. “I do believe the agency was underfunded for many years, and the task of regulating these enormously diverse and important and complex markets far outstripped the agency’s capabilities,” Schapiro told the subcommittee.

Over the past three years, the agency has been overhauled, she said. In prepared testimony, she said the SEC has improved its internal financial controls, hired people with industry expertise and targeted its examinations of investment firms based on risks.

Schapiro noted that the agency draws its funds from fees levied on industry, not from the U.S. Treasury.

Meanwhile Tuesday, on a party-line vote, the House Financial Services Committee’s Republican majority rejected a nonbinding proposal by Rep. Barney Frank (D-Mass.) to endorse the Obama administration’s $1.6 billion request for the SEC. In an advisory message about the SEC’s budget, the committee invoked the Madoff debacle, among others.

In an interview, Frank said Republicans were talking about “the old SEC,” and “part of the reason you don’t catch things is you don’t have enough people to catch them.”

The wide-ranging appropriations hearing touched on the so-called Volcker Rule, a congressionally mandated measure that restricts banks’ ability to engage in financial speculation. The SEC and other regulators must translate it into a detailed rule, and their proposal has met considerable opposition.

Rep. Mario Diaz-Balart (R-Fla.) asked whether it would be best to “pretty much go back to the drawing board and start all over again.”

“Whether we start right from the beginning again or not, I can tell you that we will very carefully and are very carefully reviewing the comment letters . . . and rethinking how we should approach the statutory requirement,” Schapiro said.