Vespa's aren't that easy to knock over from the side due to the fairly wide center stand, but if knocked from the rear it's a different story because of the preloaded springs always wanting to pull the stand upwards on its hinges. Or from another perspective, because of the springs that are constantly trying to cam the bike forward off the stand, and since there's no 'parking brake' on the rear wheel, you should be able to imagine what could happen.
I know this from experience when an adult, not a child, accidentally bumped my PX from the rear while moving boxes and was horrified to watch it cam itself over the center stand and promptly fall on its side.
A sure-fire fix for this is to cobble together a box shape that slides in between the rear wheel and the legs of the stand. As long as as it prevents the stand from getting closer to the wheel, it's near impossible to roll forward off the stand.
Another solution might be to simply make sure to park it in gear and not neutral, but I haven't tested this.
Attached are a couple of old pics of what I threw together at the time.
