There are several reasons why Argentina did not continue to be as prosperous later in the 20th Century as it was earlier. It's importan to understand the basis of early Argentinan prosperity and why it did not continue.
First, Argentina's early prosperity was based on exporting agricultural products to Europe. It used foreign (primarily British) capital and technology to improve its agricultural production. British paid for the railroads, refrigeration technology, and brought in advances in cattle breeding, fencing, seed selection, and processing technologies that increased Argentiean productivity. Argentinean manufacturing provided for the domestic market only under a protective tariff for import substitution.
In the early 20th Century, this was enough to build a fairly prosperous economy. But it was vulnerable to changing conditions because of these weaknesses:
1) It relied on Argentina earning lots of cash through its export of agricultural products.
2) Argentina was heavily reliant on foreign capital. Not only does that mean money for improvements were dependant on the international financial markets, it also meant Argentina did not control the development of its own infrastructure as foreign businessmen's purpose was not to develop the Argentine economy, but to make their own investments profitable.
3) Argentina was heavily reliant on foreigns for improved technology and commercial knowledge.
4) Argentina did not have a large enough domestic market to sustain a competitive industry and enjoy economies of scale in comparison to other countries.
5) Argentina's government, although a nominal democracy, never had a strong tradition of the rule of law which limited the powers of government, kept rulers in check, and discouraged corruption.
6) The Argentine economy was not prosperous enough to pay for a large social welfare state along European lines.
Under Peron, all these weaknesses came into play. Peron wanted to build a welfare state that was beyond Argentina's ability to pay. His short term solution was to seize control of export revenues to increase government income. By limiting the ability of exporters to earn money, he gave them a big disincentive to invest in more productive technology and managerial knowledge. This made the economy less dynamic. As technology improved around the world, Argentine industry became even less competitive. Which meant for political reasons it needed even more protection. But subsidies encourage inefficiency, and higher import duties meant Argentinean companies could less afford the needed foreign technology that would help them become more competitive. Furthermore, the lack of rule of law meant Peron could stay in power for a long time to perpetuate his bad policies despite the growing corruption. This is a simplified version of what happened, but it gives us some insight on what needs to be avoided.
A) Argentina must eliminate export taxes and controls so that its export industries can continue to grow.
B) Argentina needs to keep its access to the international credit markets while encouraging the growth of its own financial centers. It needs to create the kind of banking regulations that would transform it into a financial capital of Latin America.
C) It needs to fun its own plan of internal improvements to encourage economic development across the country. Which means it needs to increase taxes to pay for the new infrastructure. Presumably, a long term plan is needed to prioritize what gets built first as it won't be able to pay for eveerything it needs.
D) It needs to encourage technological development through easier access to foreign machine tools, and encourage indigenous know-how by boosting engineering education and other craft skills.
E) It needs to expand its home market in order for its industries to enjoy economies of scale. Some kind of greater Southern Cone customs union would be good, possibly including Brazil. Mercosur a few decades earlier.
F) Strengthen the rule of law, encourage strong separation of powers, punish corruption.
G) Determine the proper level of welfare state that Argentina can have based on existing revenues, and don't increase it until economy has grown enough to pay for it. Anything more will simply hurt the economy too much and end up eating the seed corn.
It needs to have an outward looking, dynamic economy. Unfortunately, this is everything the "experts" think won't work after WWII. although Peron himself did much harm, even without him Argentina would need to change some things as the conditions of the early 20th Century no longer applied postwar.
But it can be done. It would require a lot of things changing though, perhaps changing the 1930 Coup (as JFP suggested) or something else earlier could butterfly a lot of the needed things.