from that link i gather that you screw these parts into a base of some sort, then pound the "snot" out of some piece of metal. So you probably aren't installing them with a singificant preload, enough to tighten them up. But if you're pushing up on the end of the punch, isn't the thread transferring the load in bending ? hence tension stresses. Further, if it is a machined thread, the stress concentration is much higher (than for a rolled thread).
Is there a picture of a new punch tool?
There is a narrow stripe worn in the green flange face. It appears to only go part way 'round the threaded hole, like there was a small flange on the punch tool. By small I mean a little larger than the thread major diameter.
There are signs of fretting corrosion on the lower half of the shoulder and on the threads. Bending fatigue can be initiated from cracks induced by the fretting. Check out the following web site and it's links.