This confuses me too.
Did the queen once mate with one of these males and save the sperm for two years? Or are the queens somehow born with a copy of the genetic material.
Or does the old queen produce one, which mates with the new queen, and then dies off. And the new queen is able to hold onto that sperm for years (forever?). And they only produce a handful of males for this purpose?
Also why is it so difficult to have males in lab conditions?