Can anyone here suggest a plausible scenario that would have allowed a native nation to survive until modern times?
Bonus points: what about North and South American civilizations?
So this straddles the edge of our rule on hypothetical questions, since it's really impossible to say anything with authority about "what-if" scenarios. They were conquered, and it's really impossible to say what conditions would have prevented that. There were a few minor success stories. Tayasal (or Noj Peten), for example, was the last Mesoamerican city-state to fall and it held out until 1697. That wasn't because of any particular strategy they employed, it's because they were in a remote region where the Spanish government wasn't able to exert much direct control.
I can however say a bit about why they were conquered, so let me make a few observations that I think you should consider:
Epidemic diseases, especially smallpox, hit Mesoamerica particularly hard. Even by the standards of other epidemics within the New World, the population decline was staggering. At the low end estimate, Mexico and Central America lost about 30% of their population within the first few years, and 75% over the first century. At the high end estimate, those two numbers go up to 50% and 95% respectively. The high population density of the region, the lack of prior exposure to smallpox, and the fact that they were a main target of early colonialism made this virtually unavoidable. Following the first smallpox outbreak, other diseases thrived taking advantage of people's weakened immune systems.
The Spanish were absolutely determined to conquer them. There's a document called el requerimiento that the Spanish government produced that was essentially a declaration of the intentions of the conquistadors. An English translation is available on the wikipedia page, and it's worth a read, as it really explains their mindset. In a nutshell, the document says that the Pope was appointed by God as the supreme ruler of humanity, and has authority over all men even if they've never heard of him. The pope ruled that the peoples of the New World were to be subjects of the Spanish crown, ergo they were already subjects of the Spanish in the eyes of God. Therefore, if the natives resisted they were not soldiers defending their country, but subjects in rebellion against their rightful sovereign, and would be punished as such. Individual conquistadors could have been killed, and individual attempts at conquest may have failed (and did, in some occasions). But in the long run, the Spanish were not really willing to recognize native sovereignty and weren't likely to give up.
Native states and empires had long held animosities with each other, and were not willing to cooperate with each other against the Spanish. It's well established that Cortés and Pizarro largely depended on native allies to succeed. A question that often comes up is why would these people not unite in the face of a foreign invader. The fact is that each of the native states in Mesoamerica was a different country, and saw themselves as such. There were a few historical figures, like Xicotencatl the Younger, who seemed to have a gift of foresight about what the Spanish were trying to do, but they were in the minority. To the Tlaxcalans and the Tarascans, the Spanish were fighting the Aztecs, who were their enemies. The idea of "Europeans" versus "natives" was simply not how the natives saw things.
Do all of these things make the conquests of Mesoamerican states inevitable? Who knows, but these were broad and pervasive trends that characterized the Spanish conquests in Latin America. Getting rid of any of these factors would only be plausible in an alternate history. In real life, this is what happened.