Yeah mine have popped out a couple of times when bending too far forward.
As for the shoes… probably unrepairable I think. Its more than a worn heel. You must be …. no offence… slightly bow-legged …(most of us are.) So your weight presses on the outside of your shoes, which weakens their structural integrity over time such that your centre of gravity is no longer immediately above the mid-line of the shoe anymore. You have got a tilt to the outside edge. If you take a close look you might see this. This is what inevitably happens to my heels after wearing them for some time.