Welp, you realize that you have control over what segments seem to be hidden and which don't... at least insofar as your own view of yours and others people's activities in Strava.  On the web, bring up a run activity, click 'segments' in the upper left, then move the cursor down the list of segments. To the right of gap and elevation the word 'hide' or 'unhide' will appear. That should stick for all viewing, at least it does for cycling.  
As far as why a segment gets hidden automatically... it probably had to do with how many people complete, "star" or "hide"  or "unhide" that segment... those are probably tallied up like votes behind the scenes.   

I do realize that. However I never hide segments myself. And, unless you open an activity on Strava web, you can’t even see that there are any hidden segments. They just vanish. They don’t appear on the map either when you browse segments in the area.

Nevertheless, segment become hidden on their own, and that is what I would like to understand and prevent. Imagine the following, I am planning a weekend run and I want to target a few segments to be synced to my watch as live segments. But hidden segments are nowhere to be found. If I want to find them, first I have to remember that there was a segment. Then I have to find an old activity with that segment, open it on Strava web, and unhide the segment. How is that user friendly?

You do have a point, there.

I don’t buy this. This particular segment that I shared above is starred by 6 people. I looked at other segments in the same area, and none of them are starred and they are still visible. I think this has more to do with what Strava considers segment popularity, which includes how many people matched the segment. But this popularity metric is flawed because it naturally prefers shorter segments because shorter segments are just more likely to be matched. What I’ve noticed before that Strava tends to hide longer segments.