I did do the research! :)
This scientific site says it lasts 100 years!
I would think that, outdoors, exposed to the elements, the urushiol would only be allergenic to humans for something on the order of perhaps only 5 or 10 years, but, the point is that the oil from Toxicodendron diversilobum will last far longer than we'd like it to.
The verbatim statement from that web site below leads me to conjure the thought that this single plant on my property can infect every single person on earth, since it was literally dripping drops of sap within a few minutes of cutting the plant! "Urushiol is so incredibly toxic that it would take only one ounce of it to affect everyone on the earth with a rash (Brooks 2001)."