Answer:
The weakness of the colonizer
Explanation:
The indepence movements arise at a moment when the former empires have lost its over-all control of their colonies because of internal conflicts and economic downfall. This of course is not the only factor but it sure has been one of the most important ones. If we look at Spain we´ll see that as early as the 17th century the Iberian empire is starting to crumble - Antonio García de León, from a Mexican point of view, explains in several books and articles ( Economía y vida cotidiana en el Veracruz del siglo 17) why.
After Napoleon invaded Spain in the beginning of the 19th century the once so powerful Iberian empire was completely lost and divided. It was the moment for people like Simon Bolivar to try their luck.