When the Keepers demonstrated their power by making Los Angeles disappear, Stuckey was able to see the wave of black slowly advancing from the south. He called Allister Greaves to describe the phenomenon, and then went to investigate in person.
Stuckey got too close, and discovered he could not get away, and was swept up in the enormous cold. The last thing he heard was the blood cells freezing and popping in his heart.
Los Angeles was later returned unharmed, and Stuckey is presumably doing fine.
Stuckey was clearly intended to die, but when writer David Cian took over for Scott Ciencin, Los Angeles's destruction -and Stuckey's death- was softened to merely 'cut off from the outside world for a while.'
The nuclear explosion actually took place off the shore of San Francisco in Prime Directive, a persistent oddity in the Keepers Trilogy.