First, why the market share of IE is so resilient to die? Second, why did IE lose to Chrome from the position of market domination while Windows has always been dominating the desktop OS market? Now I realized that the answers to the two questions are the same — the mechanism of the software update.
This can't be right though, because IE always had updates too, via Windows Update. Although they weren't as frequent as Chrome's
The answer of why IE hung around for so long probably has to do with corporate intranets and Microsofts huge enterprise customers needing to preserve backwards compatibility. Backwards compatibility is one of Microsoft's strengths but with IE it became a weakness for them.
The answer of why it lost to Chrome is that Chrome was a very strong entrant in the battle from day 1 of its release. Remember the Chrome launch comic? https://www.google.com/googlebooks/chrome/index.html