Did I say impossible? I said "statistically very difficult", which is a different thing.
Btw, I looked around for an embassy of the Mauryan empire but wasn't able to find it

Out of the joke, even 4 good kings were not enough: the Mauryan empire lasted 4 centuries, which is a very impressive achievement, but even after this series of lucky draws 50 years of weak kings were enough to destroy it.
Which is par for the course: a dynasty raises, last a couple of centuries (or maybe even 4, never mind) and then falls; sometimes a new dynasty picks up the pieces and builds again an empire, sometimes it does not.
Persia is a case in point: the Persian empire rose and failed multiple times, but in the end there was always an Iran (even after a cataclysmic even like the Arab invasion which changed the religion of the country or the Mongol invasion with the associated destruction of infrastructures).
There has never been, however, a dynasty which lasted a whole millennium (which, funnily enough, was achieved by a republican state, the Serenissima Republic of Venice): food for thought.