I don't know how your bottom plate is secured to the floor but old timers used to drive a steel spike or piece of rebar type material on the outside of the bottom plate to keep it from kicking out. A few of those couldn't hurt either.
The bottom piece of lumber is secured to the floor with 5/8 inch concrete anchors. You may mean the bottom plate of each stud. If so, these are secured with screws into the bottom piece of lumber that lies along the floor. These may be my newest weak point . I'm going for the lumber now for reinforcement. I'll look to see what I can do to support the bottom plate holding each stud in place.