An alternate history cliché of sorts.
For some reason or other, works in the genre of alternate history - outside those written by actual South American authors - often don't bother to include even a passing mention of what's been going on in South America ever since the timeline diverged from our history. If South America is ever mentioned, a few events regarding the Spanish and Portuguese colonial empires (or their downfall) might get referenced… And that's pretty much it.
Of course, not every timeline has to include South America (or most of the world's continents and geographical areas) by default. Some TLs have a deliberately narrower scope, so they can focus more on events in a specific region or country, while only briefly mentioning the bigger picture. That is excusable. But if a timeline generally strives to show the global picture as much as possible, the omission or trivialization of South America in world affairs can be really jarring as the years go by. Often, if very little attention is paid to South America in a timeline, its status may end up as one giant Citroen DS Incident. South America just seems to get the short end of the stick far too often…
Though this problem is most pervasive in the case of this continent, it can also be applied to Africa (nearly as often, especially the little attention paid to some parts of the continent), Oceania (nearly non-existent in timelines that are not set in Australia and New Zealand), the Caribbean (nearly no significance in TLs) and parts of Asia (indeed, some are harder to research and write about, but even many of the easily researched ones seldom make appearances).
Some AH.commers also dislike the lack of South American timelines and have even openly expressed this disappointment from time to time.
maverick's South America TLs, mainly about Argentina, Chile and the southern parts of the continent in general.
Max's Chaos TL has some generally interesting stuff going on in SA. It helps that the world of the TL diverged from ours already in the High Middle Ages. Among the many changes, there's a Hollywood analogue in place of OTL Rio de Janeiro.
robertp6165's The Guns of the Tawantinsuya is a very heavy aversion, since the Incas develop rudimentary gunpowder and firearms prior to the arrival of Europeans. Once the conquistadors come, they get repelled quite successfully and the longer lived Incan empire renders much of South American colonial history and politics completely different to OTL.
Thande's Look to the West doesn't skimp on the South American relevance. In-timeline, the continent even seems to develop a reputation for sparking world wars out of proportion to its importance (for instance, the Popular Wars, the opening phase of which involves a Brazilian revolution and an ensuing invasion by a rogue Dutch West India Company commander).
Pkmatrix's A Revised History of the Future spends some time discussing South America as they emerge as a unified major power and close ally of the United States by the end of the 21st Century. His timeline The Birdmen of Patagonia is set entirely in South America, detailing the first contact between Spanish Conquistadors and a civilization of large sapient birds.
In Jared's Decades of Darkness, something is definitely happening there… as in, the *US meddles in a Brazilian Civil War between monarchists/slaveholders and republicans/slavery opponents (and so does Germany, on the other side) and later expands until they reach down to Tierra del Fuego. Even later, they split up Brazil into three parts… yeah, just because the cliche is avoided, South America isn't necessarily better off.