I think I figured it out. It sounds really silly now that I see it. It was a problem with the low stiffness of the springs. When the spring force couldn't resist the applied force any more, the system failed and springs plus spherical joint went through the base plate in a snap. I increased the stiffness and it gives me a proper behavior. 
It was right in front of me and I didn't see it. 

Thank you again Mr Newman for taking the time out to reply to my question.