I don't know that I can answer the question as written for "most of Latin America, from what appears to be independence to the present day", but I think I can point to some important differences that might help you think about the question you're asking. For the sake of brevity I'll stick to Spanish America, because Brazil is a whole different thing, and I'll just refer to "America" in your question as the US.

• The independence of the United States was a purposeful, top-down effort led by a motivated elite; it was deeply rooted in international instability, but not, I would argue, primarily caused by it. The independence of Spanish America was, in large part, a product of a power vacuum created by Napoleon's sudden conquest of Spain. In the important power centers of Spanish America, this meant that various groups surged uncertainly into authority over the 15-20 years of Napoleonic instability, including an explosive, highly intolerant attempt to re-assert authority by the recently restored Ferdinand VII with the support of other counter-revolutionary European regimes. So while in the British colonies you had a relatively brief period of war with a decisive end, and a (weak, but functional in important ways) independence government with reasonable legitimacy waiting to step in, in Spanish America the best case scenario was to be far enough away from a power/economic center that you were mostly left alone for the decades of warfare and disorder. Which creates a neat catch-22 since those remote locations like Costa Rica were not going to become the sort of regional powers people have in mind when they ask this question. Because we lack (afaik) comprehensive evidence for how generalized support for US independence was, it's tough to really track that ebb and flow, but as you'll see in the next points, at least it wasn't like the upper classes were hopelessly alienated from the middle and lower classes in terms of their goals, which were basically "change as little as possible and don't give an inch to the poor or underprivileged" more than broad ideas of independence. Why was this?

• The power vacuum situation in South America meant that, for all practical purposes, South America's major countries were simultaneously embroiled in the equivalent of the US Revolution and Civil War, at the same time, for a period of at least two decades on-and-off. That means issues of race, caste, class were being negotiated (Bolivar's rebranded independence movement after Haiti, Mexico's Hidalgo vs Iturbide branching paths, Peru's post Tupac Amaru II mentality was firmly in place, etc) simultaneously with basic questions of chain of command, forms of government, economic structure. This meant that people who Had Stuff in Spanish Latin America felt they were in a very scary place compared to US elites, and you can easily see why competing thrusts at low-consensus republics that shut out these new ideas or military dictatorships coming in and out of power would lead to difficult precedents, and far from "taking care" of major questions of governance like the eventual US Civil War, really only set in place the potential for cyclical discord, often tied to individuals rather than institutions, in many countries (see: caudillismo).

• Timing. Ideologically, the Euro-American world was a very different place in the early 19th century versus late 18th, due in no small part to the US revolution but also to the French Revolution and, importantly, the semi-successful revolt of enslaved persons in Haiti. Combined with the uncertainty and the outbursts of change in social order in various independence movements (again, Hidalgo and the undercurrents that would lead to Bolivar v2), and you have that situation I described in the first point. Which is that the leadership that would take power from Ferdinand VII's (unwilling) hands was, in most ways, profoundly conservative and reactionary in motivations that simply weren't present for US leaders/elites in their ascension to power.

I could go on, but that gives you three big things I think are important in considering the process of independence in the two regions. Why things evolved differently from there would really benefit from a country by country breakdown, as (for instance) Mexico's evolution into its 19th century and 20th century forms is much more deeply enmeshed with American intervention than, say, Argentina, to cite just one important factor in its "instability" over time. Apologies for the big generalizations above, but I hope they get the job done.

Further reading: Rodríguez, Jaime E. The Independence of Spanish America. Cambridge University Press, 1998. Halperin-Donghi, Tulio. The Aftermath of Revolution in Latin America. Harper Torchbooks, 1973. Bulmer-Thomas, Victor. The Economic History of Latin America since Independence. 2nd ed. Cambridge University Press, 2003.

Some more specific works that do well addressing this question in their areas Woodward, Ralph Lee. Central America: A Nation Divided. 3rd ed. Oxford University Press, USA, 1999. Walker, Charles F. Smoldering Ashes: Cuzco and the Creation of Republican Peru, 1780-1840. Duke University Press Books, 1999. Young, Eric Van. The Other Rebellion: Popular Violence, Ideology, and the Mexican Struggle for Independence, 1810-1821. 1st ed. Stanford University Press, 2002. Jiménez, Iván Molina, and Steven Paul Palmer. El paso del cometa: estado, política social y culturas populares en Costa Rica (1800-1950). Editorial Universidad Estatal a Distancia, 1994.

While I know Niall Ferguson is not the most unbiased person out there, I would at least bring out a point he makes about northern american British colonies compared to Latin american colonies. He argues that in British colonies, more people owned land, property rights were better enforced and there existed a more representative method of government for the landowners. New colonists could also settle new lands and become new landowners, which was much less the case in Latin America, where huge swaths of land were owned by nobles/landowners. This meant that it was possible for people to rise from being a poor immigrant to a landowning and vote-casting member of the society. He then argues that this democratic government with the rule of law led to economic prosperity and greater stability.

Another point i was taught in geography lessons back in high-school was that while the Latin-American colonies were mostly extraction-type colonies (a relatively small european population with a lot of native and African slaves extracting either metals, wood or crops from the land to be sent to the centres of their respective empires, North-American colonies had more European populations, that tried and wanted to distance themselves from their homelands (often fleeing persecution and poverty) which led to more self-sufficient economies. This later led to rising industry and a diversified economy. After independence the latin american nations largely retained their etraction-based economy that has a lower potential added value than a diversified and industrious society that the north-American economy evolved into. This diversified economy allowed more people to enrich themselves (not only had you to own lots of land and slaves to become succesful), but there existed other ways to create wealth (working as a payed worker in industry, agriculture, construction).

Which Latin America? We all have different histories you know.

So I come at this from a background in political science and law. I would point out that America wasn't exactly stable or dominant until after the World Wars. The pre war history seems full of violence, insurrection, riots, economic depression, political suppression, and all the other hallmarks of a generally rough place. Land mass, resources, recent and massive industrialization, and the fact that Europe was in shambles after the wars allowed America to assume the role of a global superpower. But it wasn't always coming up roses. By contrast, I remember studying how the post-revolutionary regimes in Latin America generally took an authoritarian form, where industry and decentralized power structures combined with small land area to produce an environment where supression was used as a tool for development, by a coalition of military leaders and technocratic elites. The idea of decentralization seems to trace all the way back to Spanish colonization, where again population control and rule-by-elites was paramount for maintaining a steady flow of raw material exports. I have always personally considered the later-arising "bureaucratic authoritarianism," as it is commonly described, to be a product of anti-idealist regimes that want to play "catch up" with more developed powers, with a pragmatic approach that views civil liberties as secondary to economic growth.

Of course, through a modern lens, we can't discount the negative effect, intentional or not, of having the United States looming over the back yard. Many regime changes that have occured in the region were sponsored by the American government, but always as a tool for promoting solely American interests - not the creation of stable governing structures.

Just some thoughts! It is a very complicated question.

Well, first we need to understand what is a stable republic. How many north american presidents were murdered? I don't see this as a stable republic. North American democracy is for a few people.

Having said that, latin american were raised in the condition of extraction-type colonies and there were no interest on those who had power to give better conditions to the people or to cut these explorations from the developed countries leaving us economic and political dependent and eternally on the sub-developed condition.

I highly recommend Economic Development of Latin America by Celso Furtado, one of the best thinkers in Brazil.

"Why Nations Fail" attempts to answer that question. It's too broad for there to be a clear cut answer accepted by everyone.