Standard measures of the U.S. labor market look pretty good. The unemployment rate is low, and job growth has been steady. But one indicator is flashing signs of fragility.

It's an important one, too: The Federal Reserve's Labor Market Conditions Index. After falling just three times from 2012 to 2015, the index has fallen every month of 2016 except for one, July. And in July the annual change in the LMCI, from July 2015, turned negative.

That's only the eighth time in nearly 40 years the index was down on a year-over-year basis, Deutsche Bank Chief U.S. Economist Joseph LaVorgna wrote in a note to clients today. Of the seven previous occasions, LaVorgna wrote, "four were soon followed by recession."

(In the three other cases, two were false alarms, in 1986-87 and 1995-96, and in 1981 the recession began shortly before the annual change in the LMCI turned negative.)

LaVorgna said the weakness in the LMCI indicates a rising possibility of recession. 

"The upshot is that the economic outlook remains fragile despite the ostensible robustness of the labor market," he wrote.

In September the index fell 2.2 points. The October reading will be released Nov. 7, one day before the election. 

The Labor Market Conditions Index is made up of 19 indicators, including the unemployment rate, average hourly earnings, the labor-force participation rate, and less-followed measures such as a help-wanted index, temp jobs, and the length of the average workweek.