The median spell of poverty in the US is about six months. That's my guess, based on the latest government stats I could find, as represented below:

Source: https://www.census.gov/newsroom/blogs/random-samplings/2014/01/using-the-survey-of-income-and-program-

My guess is a little lower than what's shown in the graph, because the unemployment rate during 2009-2011 was twice as high then than it is now.

Poverty isn't a permanent condition for the vast majority of Americans.  Even during the years of high unemployment after the Great Recession, just 2.7% of the population were classified by the Census Bureau as living in chronic poverty. There is, however, a larger subset of individuals who hover around the poverty line much of their lives, falling down and picking themselves up, again and again. I suspect most lack serious education or training past high school, meaning completion of at least an associates degree or vocational training certificate.

Poverty data can be misleading. When we read that 14.5% of Americans are living in poverty, that doesn't mean that 14.5% are "stuck below poverty line", to quote a Huffington Post headline.  To be "stuck" implies a chronic condition, as if that 14.5% were the same people from year to year. They're not. 

Those who are truly stuck in poverty need different kinds of government help than those are suffering brief periods of hardship. That's why it's important to know what the numbers mean.   When voters misunderstand data and make false assumptions about the nature of a problem, they elect politicians with dumb ideas on how to fix the problem. And so the war on poverty continues.