Once I pushed the release button too much and it got stuck on the bottom. Same thing as you have, the stem did not stay inside any more.
I put just a little bit of oil on the tip of a needle and dropped it on the release button. It worked! The button came back up and after that everything worked well.
I didn't want to crap on your sales thread here, but in that thread you say it's a keyless issue. Is that the same watch you're talking about here? I get the impression that you already tried fixing the keyless issue on this watch and weren't able to resolve it. Would it be safe to say that it's more than a keyless issue?