The fraction of workers willing to quit their jobs is stuck. It was 1.6 percent in June, the Bureau of Labor Statistics announced on Tuesday, unchanged from the previous month and from the year before.

That’s unwelcome news, especially coming after a few months of weak overall job growth. Low quit rates are an indication that workers don’t think the labor market is in good shape and are fearful of losing their current jobs.

The quit rate regularly exceeded 2 percent before the recession, but has only recovered slightly five years after it began plummeting and eventually bottomed out at 1.2 percent in 2009. Over the past year, its ascent back toward normal levels seems to have stalled out.

The quit rate is reported in the Job Openings and Labor Turnover Survey, published monthly by the BLS. Although the survey, known as JOLTS, doesn’t get the attention that the monthly jobs report does, key policymakers keep an eye on it to get a sense of the latest trends. Janet Yellen, the vice chairman of the Federal Reserve who has been mentioned by President Obama as a possible replacement for current Chairman Ben Bernanke when his term expires in January, has said that she monitors JOLTS data to inform decisions about the money supply.

Tuesday’s JOLTS release was underwhelming overall: total job openings rose to 3.9 million, an increase of just 29,000 over May’s number. For every job opening in June, there were three unemployed workers. That’s a vast improvement since the worst days of the crisis in 2009, when there were more than six job-seekers for every opening. But when the recession began, there were just 1.8 unemployed workers per posting.

The number of workers hired actually fell, from 4.5 million in May to 4.2 million in June. In June 2012, 4.4 million people got new jobs. The number, which includes government jobs, was regularly above 5 million before the recession began.

Overall, labor market “churn” remains depressed and shows only few signs of improvement. Based on hiring and firing dynamics, there is little reason to think that overall job growth will accelerate above the recent tepid 180,000 pace in upcoming months.