A trove of data released by the Education Department on Monday shows a continuing trend of people enrolling in the government’s generous student loan repayment plans as well as people struggling to pay their debt.

Americans have a wealth of options for repaying their student loans, because of the Obama administration’s expansion of programs that cap monthly payments to a percentage of earnings, known as income-based repayment plans. Few people initially knew of the plans, but direct outreach and marketing campaigns have quadrupled enrollment in the past four years.

As of the end of June, nearly 5.3 million people were enrolled in the plans, a 36 percent increase from the same period a year before and a 110 percent increase from two years ago. Enrollment in the newest plan, known as Revised Pay as You Earn, or REPAYE, tripled in the last quarter to 570,000 borrowers. The program caps borrowers’ monthly bills to 10 percent of their income and forgives the debt after 20 years of payment for anyone with what’s known as a direct federal loan, regardless of their income or when they borrowed.

The point of income-driven repayment plans is to help people avoid defaulting on their loans, which could ruin their credit and make it difficult to buy a home or a car. While the surge in enrollment in income-driven plans is a win for the White House, the persistent level of defaults signals a disconnect somewhere in the servicing of federal student loans.

According to the Education Department, 8.1 million people — roughly the population of New York City — had not made a payment on $128 billion in student loans for at least nine months as of June, an 8 percent increase over the same period a year earlier. Well over half of the people in default have loans from the old bank-based federal lending program, but the number of borrowers with newer loans who were falling behind on payments is high.

Matt Sessa, a deputy chief operating officer at the department, said in a statement that the portfolio of defaults continues to grow, even as delinquencies and new defaults have declined, because defaulted loans are rarely written off. He said the number of people defaulting for the first time has decreased as a percentage of borrowers in repayment — the total universe of borrowers repaying their loans — crept up in the last quarter.

Still, tens of thousands of people are defaulting for at least the second time.

The government pays student-loan servicers, the middlemen who collect and apply payments, hundreds of millions of dollars to help people stay current on their payments and avoid default. And the suite of income-driven plans is supposed to play a key role in that effort, yet a report released last week by the Consumer Financial Protection Bureau said servicers are falling down on the job.

People trying to enroll in income-driven plans have complained to the bureau of prolonged processing delays and wrongful rejections by their loan servicers. Those delays and rejections can result in increased interest charges and lost eligibility for some federal benefits and protections, according to the CFPB.

“Student loan servicing breakdowns can stack thousands of dollars of hidden costs on the backs of borrowers who can least afford them,” the CFPB’s student-loan ombudsman, Seth Frotman, said in a statement. “Too many student loan borrowers are struggling to take advantage of their right to pay based on how much money they make.”

The complaints the bureau tracked dovetail with accounts from consumer advocates who earlier in the year raised concerns about the problems borrowers were having enrolling in REPAYE. In the spring, advocacy groups said servicers were unprepared for the volume of applications, leading to months of processing delays and backlogs. They said it took 30 to 60 days longer to get enrolled in the new plan, and while some borrowers wait, their monthly bills increased as servicers temporarily place them in standard repayment plans.

The Government Accountability Office also has highlighted problems in student loan servicing that may be contributing to borrowers’ struggles managing their loans. Researchers found that 70 percent of people in default actually qualified for a lower monthly payment through income-driven plans that cap monthly payments to a percentage of earnings but that servicers are failing to provide sufficient information about the options. Even when the contractors contact to delinquent borrowers, the information is often inconsistent.

Loan servicers have argued that they deploy all of their resources to catch borrowers before they default but that mailers, calls and emails often go ignored. And until recently, there have been no market-wide federal rules for how servicers are supposed to operate.

Want to read more about the student loan servicing? Check out these stories:

The provision in the budget agreement that could radically change student loan servicing

How the attempt to fix student loans got bogged down by the middlemen

A guide to paying off your student loans