Even though consumers are digging deeper to cover rising out-of-pocket medical costs, they’re contributing less to health savings accounts that could help take the sting out of their expenses, according to a new study.

Between 2011 and 2014, the percentage of people who said they contributed nothing to their health savings accounts (HSAs) more than doubled, to 23 percent, according to a survey by the Employee Benefit Research Institute. Meanwhile, the percentage who said they contributed $1,500 or more dropped to 30 percent from 44 percent.

While the reasons for the decline in contributions are unclear, “one of the things to consider is that these plans have been around for a while now and at some point people may stop contributing if they’ve built up an account balance,” says Paul Fronstin, director of EBRI’s health research and education program. For example, someone with a $5,000 HSA balance whose plan has a $2,000 deductible may feel comfortable he can cover out-of-pocket costs.

Unlike flexible spending account balances, in which money is generally lost if unused at year end, HSA balances accumulate and can be used in future years even if workers change jobs.

Health savings accounts were established in 2003 as a way for people to save for future out-of-pocket medical expenses. The money is deposited, accumulates and can be withdrawn tax free. The accounts must be linked to a health plan with a deductible of at least $1,300 for individual coverage and $2,600 for family coverage in 2015.

Employers often contribute to workers’ health savings accounts, but the EBRI analysis found that their contributions declined as well. Sixty-seven percent of workers said they received employer contributions in 2014, down from 71 percent in 2013. EBRI’s analysis included both HSAs and health reimbursement arrangements, another type of account to which only employers contribute money for their workers’ health care expenses. In addition, the funds belong to the employer.

As employers continue to shift more health care expenses onto workers’ shoulders, offering high-deductible plans that link to financial accounts has become increasingly popular.

In 2014, 73 percent of companies with more than 1,000 workers offered an account-based health plan, up from 51 percent in 2009, according to the Towers Watson/National Business Group on Health annual employer health care survey. A third of workers at those companies were enrolled in such accounts in 2014, the survey found, more than double the median 14 percent that were enrolled five years earlier.

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