You have a presta stem where it's possible to add stem extensions to increase stem length. You are removing the Presta's main valve body from the factory stem because the manufacturer leaves these incompletely torqued for whatever reason. You also appear to be using an adapter (the silver piece with gasket in your photo) that attaches to the presta valve, converting it for use with a pump set-up for Schrader valves. When one unthreads this adapter (all the ones I've dealt with screw on, they can't just be pushed on), if you've torqued the adapter greater than the torque of the valve body, the valve body threads to the stem will yield first, the adapter stays on the valve body, and the next thing you hear is the hiss of air. That gasket also contributes to the problem by gripping the valve body.
First, there are typically wrench flats on the valve body. Sometimes in the threaded area. Yours are likely to be found at that gap in the threads of the valve body. Reinsert the body any hand tighten it. Often times the max torque you can achieve with your fingers is tight enough to keep the body in place using the adapter. Needle nose pliers work well in that tight area of the flat in lieu of a small enough wrench. Somebody's idea of loctite isn't a bad idea, but I wouldn't purchase any for this task. Part of my airing up process is giving the valve body a firm twist right to check tightness between removing the cap and opening the valve. I'd also suggest to put the adapter on the opened stem first, then attaching the pump to the adapter to better gauge and control the torque at the stem-adapter interface. IDK it's a minor point and may work better the other way. I typically use an air chuck you push onto the adapter to get air--same as filling a car tire. The key to it all is not getting the adapter tighter than the valve body. Many pumps these days have ends that are themselves adaptable to either Schrader or Presta valves using the same parts of the connecting end configured in different ways. See if that's possible with your pump, set it up for Presta and eliminate the adapter.