Dear Vitaliy,
this is an absolutely amazing post!!! It would have been nice to have these graphics in my history classes back at school.
As you say RANK vs LIFETIME in a log-log for a large range there is a power-law like behaviour. It is actually interesting to look at the countries that did better than that. What did they do differently? It also appears that the half life time of countries/empires becomes shorter over time; there might be a strong selection bias though.
This is a really beautiful piece of work. Thanks for posting.
Marco