Well, the reason why Firefox and Chrome did well was because Microsoft just stopped trying with IE. Had Microsoft updated their browser with the same level of effort as they do today, I don't think we would have seen the 2nd browser war.
You may be putting the cart before the horse. Microsoft stopped pushing IE because there was no competition. Once the competition materialized, IE started moving forward.
Without competition, Microsoft had no justification to spend the resources on enhancing IE.
In other words, IE's improvements came as a result of the development of Firefox and Chrome.