Thanks for your reply!
My crown however doesn’t look as though there is anything physically there to interact with a collet to prevent it from coming out (see picture).
It has to slide up and down inside the outer ‘sleeve’ and push on the ‘pushrod’ to allow you to change the time.
Does not appear to be broken, looks like a 2 piece stem. I believe it is supposed to be this way. There is supposed to be a collet that screws into the case that keeps the crown from slipping out.
Now you're design may be different, but this is the most typical. I have had the segments with the fine slits break off and then the stem won't stay in place anymore.