Some companies are pushing to withdraw their workers from a giant Teamsters pension plan that faces a deep funding shortfall and questions about its long-term viability.

Investment losses during the financial crisis and hard times for trucking companies that pay into the Teamsters' Central States Funds have sapped the fund of money it uses to pay promised benefits.

With just 60 cents of assets for every $1 in obligations, the Teamsters pension fund is considered in "critical" status by the Pension Benefit Guaranty Corp., the federal agency that backstops failed pensions.

Central States has about $18 billion in assets, ranking it the nation's second-largest multiemployer pension plan. Such funds get contributions from numerous companies.

The Teamsters pension fund pools money from about 1,900 companies, and its investments have been overseen by advisers jointly approved by representatives for union and management.

Recent efforts by Republic Services Inc. RSG -0.91% to pull out about 800 sanitation workers from Central States show the uphill battle facing a pension plan founded by the late Teamsters President Jimmy Hoffa.

Last week, Republic Services finalized deals with three local Teamster unions in Michigan to move out of Central States to a better-funded Teamster-run plan. Food service distributor Sysco Corp. SYY -0.19% removed its last Teamster unit from Central States in January.

"There is a reasonable possibility that this plan could run out of money in about a dozen years," Central States Executive Director Thomas Nyhan said in an interview.

More companies leaving the fund "accelerates insolvency," Mr. Nyhan said.

Central States illustrates a potential nightmare scenario for workers across the U.S.: a pension plan that is at risk of running out of money, leading to possible benefit cuts and putting strain on the federal agency that would assume the pension's liabilities.

"Our employees who participate in this failing pension fund and our Company deserve better," Catharine Ellingsen, senior vice president of human resources at Republic, said in a statement. "We intend to use all legal means at our disposal to exit Central States."

Union spokeswoman Leigh Strope said Republic is using the pension fund as a "smokescreen" to obscure what the union sees as separate problems at Republic.

She declined to comment on the financial condition of Central States, which is run independently of the union.

For decades, U.S. companies have shut down their traditional pension plans and moved workers to less generous 401(k) retirement accounts. In some cities, Republic has proposed replacing traditional pensions provided by Central States with 401(k) accounts.

"Pensions are a huge selling point for a union," says Ken Paff, national organizer of Teamsters for a Democratic Union, a group that opposes the Teamsters' leadership.

"If you take that away, you hurt the union's ability to organize workers," he said.

The price for exiting from the fund is steep. Republic estimates it must pay a "withdrawal liability" of as much as $146 million to cover the company's share of Central States' unfunded liability.

This amount could go up if the company stays in the plan and the funding level deteriorates.

Mr. Nyhan said he offered Republic protections that would eliminate future increases in the company's withdrawal liability. Other companies in the fund have adopted such measures, he said, but Republic rejected them.

Ms. Ellingsen said Republic's "employees only stand to gain in benefits by getting out of a pension fund that is going insolvent."

After investments losses from the tech bust in 2002, Central States cut retirement benefits and increased contributions from employers to shore up its funding level.

Heading into the financial crisis, Central States' had just received $6.1 billion that United Parcel Service Inc. UPS -1.12% paid in exchange for letting the company's employees out of the fund.

At the time, Central States had a large bet on the stock market—about 66% of its assets, according to Mr. Nyhan; the median stock allocation among multiemployer funds back then was 54%, according to Wilshire Trust Universe Comparison Service.

Goldman Sachs Group Inc. GS -1.17% and Northern Trust Corp. NTRS -1.95% were the pension fund's appointed fiduciaries responsible for picking money managers and setting asset allocations.

Since the recession, Central States' assets have dipped to $18 billion, from $27 billion in late 2007.

Goldman resigned from the pension plan in 2010 because the "mandate no longer fit with the company's business model," a person familiar with the bank's position said. Northern Trust is still a fiduciary, but the firm didn't respond to requests for comment.

Mr. Nyhan said he doesn't blame the banks for the steep losses. He said the fund needed to boost its returns with big stock allocations "because of the underfunded nature of the plan."

The pension plan pays about $2.8 billion in benefits a year but takes in only about $700 million in employer contributions. "You have to make up the rest with investment returns,'' said Mr. Nyhan, which he thinks is unlikely over the long term.

The recession also hurt some of the fund's largest companies, which meant smaller contributions into Central States.

Hostess Brands stopped making payments altogether, and the bankrupt maker of Twinkies owes Central States a $583 million withdrawal liability, according to pension-fund documents. A Hostess representative wasn't immediately able to comment on any pending balance.

If Central States can't afford to pay out benefits and the Pension Benefit Guaranty Corp. has to step in, some Teamster pensions would be slashed.

Under that scenario, Dave Scheidt, a retired dock loader from Kansas City, Kan., estimates his pension check would go from about $3,000 to $1,100 a month, based on federal guarantee rules.

"There are a lot of guys counting on these pensions," he says.