What half-life defines a POP (Persistent Organic Pollutant)?

Untill there is no special strain found/discoverd to decompose and degradate these compounds their half lives will be very high and can be as high as 12 up to 13 years. 

It will depend on where you would like to define the half-life of a POP, since might be years or decades in soil/sediment and a number of days in the atmosphere. In fact, it is preferred to use the word "persistent" than express a number for the half-life of POPs. 

Interesting

Chemical substances known as persistent organic pollutants (POPs) have attracted a lot of international interest in recent decades. These molecules have a unique combination of physical and chemical qualities that allow them to travel great distances, withstand degradation, and accumulate in the body. Humans and wildlife have been linked to a variety of side effects after being exposed to these substances. The role of the Stockholm Convention in supporting international efforts to identify this class of compounds, highlighted by the original identification of 12 POPs known as the Dirty Dozen. Because persistent organic pollutants are lipid soluble, they can accumulate in higher amounts (biomagnify) in species eating higher up the food chain. POPs have been identified as endocrine disruptors in wildlife investigations since the 1950s.

The Stockholm Convention on Persistent Organic Pollutants (http://www.pops.int/TheConvention/Overview/TextoftheConvention/tabid/2232/Default.aspx) in Annex D uses halflife for definition of persistence and defines as follows:

 (b) Persistence:
(i) Evidence that the half-life of the chemical in water is greater than two months, or that its half-life in soil is greater than six months, or that its half-life in sediment is greater than six months; or
(ii) Evidence that the chemical is otherwise sufficiently persistent to justify its consideration within the scope of this Convention; 

To me, the criteria for a POP should be defined by how long it takes to clear the body of the compound and reduce exposures amongst the population if we determine that a compound is more toxic than we originally thought.  I would want the exposures to reduce by a factor of 10 within 1 year.  Since it takes 3-4 half-lives to reduce exposures to less than 10% from the max concentration, I would vote for a half-life that defines a POP as anything with a half-life greater than ~3.4 months or ~100 days (12 months/3.5 months=3.4 months=~100 days).  

Pop half life is the time elapsed for  approximately dose level of exposed pop compound is metabolized and get clearance from the biological body. And also the time needed to complete degradations in the macro environment. These compounds have a very long half time in the environment and long-persistence due to they resisted decomposition and degradations