Quoting from the FAQ thread (http://www.axisandallies.org/forums/index.php?topic=28562.msg1062028#msg1062028😞
This exact question has been addressed on the FAQ (earlier thread), so I know the correct answer with certainty.
The Axis have to control 8 cities or more (or 6 for Pacific) CONTINUOUSLY for an entire round of play.
Say Italy takes over London for the Axis 8th city on I10. The Axis will win on I11 if the Allies never take (or re-take) a European victory city at any time between I10 and I11. If at any time between I10 and I11 the Axis lose a city and dip below 8, the clock has to start all over again at such time as the Axis re-claim an 8th city. If the Axis get 9 or more cities, they can lose a city and still win on I11, as long as they never dip below 8 at any time.