There are a few theories attempting to explain this. First of all, it is important to establish that other colonial powers did have grand ambitions to occupy large areas of South America.

The Netherlands, with the Groote Deseyn plan of the 17th century, probably had the most ambitious. They did occupy part of Brazil for two and a half decades, with ambitions to dislodge the Portuguese from all of it. ultimately though, the Dutch failed to gain a significant power base in Brazil, and were eventually evicted by the locals, largely without Portuguese help. This also included an ambitious plan to establish a colony in Chile, which failed to to lack of cooperation with the locals.

Notice that both these failures are not really because the Dutch were weaker than their foes, but rather a failure to gain local support. However, later the obstacles to colonizing South America would become way more structural.

To fully understand what I mean, lets look at geography. For most of hte Early Modern Period, the primary Spanish colony in South America was the Viceroyalty of Peru. This was also the economic most significant, since it supplied the silver trade that was the backbone of Spanish economic prosperity. It ran along the Pacific Coast, and for contact with Europe, it relied on the Isthmus of Panama.

This was well-known to other European colonial powers. If you wanted to threaten Spains main South American possession, it ahd to happen in the Pacific. And as the Dutch Chile expedition in 1643 shows, a lasting presence on the Pacific coast against Spain was not feasible if Spain could supply their forces through Panama, while you had to take the long route around Cape Horn. Therefore, to establish a significant presence in South America, Panama was necessary.

Now why wasn't Panama captured? It was attacked and plundered by pirates several times, famously Francis Drake and Henry Morgan. In 1698 the Scottish even attempted to establish a permanent colony there, raising great Spanish concern. The fact was that the Scottish was struck by that which became the shield of the Spanish Empire: Yellow Fever.

Yellow Fever became established in tropical America in the decades after the first epidemic of 1648 after intorduciton from Africa. It was a devastating disease, especially for newcomers, since surviving it conferred lifelong immunity. Form the mid-17th century, Spanish colonies in America were largely inhabited by people who were born there, and therefore likely survived the disease in childhood. New colonies were instead devastated by it. This happened to the Scottish colony, and it significantly happened during grand British plans to capture Spanish colonies in the 18th century, when Britain was decidedly stronger than Spain. Famously, the Battle of Cartagena de las Indias, the last major plan to capture the primary Spanish south American stronghold in the Caribbean in 1741, became a massive fiasco where a tiny Spanish force humiliated a British attacking army, largely thanks to yellow fever. Cartagena can be considered a decisive battle of world history. If Britain had captured the port, Panama would be exposed, and without Panama as a lynchpin, the whole American Empire of the Spanish was up for the grabs. But General Yellow Fever was guarding the border.

Yellow Fever was not a reliable ally however. In the early 19th century when the American colonies rebelled, Spain dispatched armies to recapture them. Now they were decimated by yellow fever, that left the native-born and therefore immune rebels largely untouched. In this way yellow fever massively shaped the history of the Americas.

I hope this was an informative reply. The yellow fever theory was thoroughly developed by John McNeill in Mosquito Empires.