Some car games I play have this issue where you would jump on a car a couple times and it would start to glitch out, probably a similar thing.
I still think it has to do with the springs. My most recent project, which I even made a post on, was a weight measuring device.
It used four springs. Perfectly balanced. If I would drop a block on it the platform would go down a bit and then stop.
However, when I would stand on the platform, it would go down, stay down for about half a second, and go up slightly.
Making the springs stiffer might change something.