Does this happen always in every airport or is it a sometime-somewhere thing?

It happened to me too once or twice, but I found out the reason.  This could very well not be the reason it happens to you, but checking doesn't hurt.

Sometimes, in some airports, when the autopilot intercepts the localizer way far from the runway, maybe for a reason of range, the glidescope needle remains inactive in the center for a while still.

So I reasoned that this is probably a bug of the autopilot that senses this kind of situation like it's already time to begin descend the glidescope.  Of course the problem is that there is NO glidescope that far away, and this brings to the problem you asked about.

And yes, in my case too pressing again the ALT hold made the autopilot ignore the glidescope when it was time to begin descend for real.

If this is the way it happens to you too my suggestion is to wait pressing the APR button on the autopilot only after both ILS needles move away from the center.

On my plane, this worked fine.