Were there common factors that allowed dictatorships to flourish? e.g. American Influence, Institutionalisation of Power, Independence, Wars etc.
I can speak for the case of Mexico, which doesn't really fit your question, but could provide some insight: During the 19th century, Mexico was submerged in a neverending civil war between conservatives and liberals, in their many different forms. After the Mexican Revolution had settled in, by 1920 or a little bit earlier, the emergence and popularity of political parties gave way to the institutionalization of authority, and this departed from the previous system of overlords who gathered parties of sympathizers to fight for a common cause and try to take over the government.
It's possible that other Latin American countries followed a similar pattern, perhaps with the advent of institutionalization coming a bit later than in Mexico's case, but I don't know that for sure though.