Brad Plummer reports on a study from the Urban Institute which purports to explain the drop in labor force participation as a story of fewer people entering the workforce after a period of being out of the workforce, as opposed to more people leaving. This explanation actually is not supported by the results shown in the study.
The study finds only a very slight falloff in the entry rate for prime age men (Table 2), even though there has been a sharp falloff in their labor force participation rate. On the other hand it shows the sharpest declines in entry for older workers, who in fact have seen a decline in labor force participation. This suggests that the study's sample is not reflecting larger labor force conditions. (The study uses the Survey on Income and Program Participation, which has a considerably smaller sample size that the Current Population Survey that is conventionally used for labor market analysis. There is likely also a problem with people dropping out of the survey, who are likely to be a particularly large share of those dropping out of the labor force.)
It's also worth noting that their analysis only looked at the falloff in labor force participation rate in one year, from 2010 to 2011. In that year we saw a drop 0.6 percentage points of a total falloff of 2.1 percentage points for prime age women and 0.7 percentage points of a total falloff of 3.4 percentage points for prime age men.