While it's more correct to say that Argentina has stopped growing (or rather, has grown very slowly compared to other economies of similar size) it is true that the picture was much different in the first half of the 20th century. Early in Argentina's industrialization there are comparable parallels to the United States: demand for both skilled and unskilled labor led both countries to welcome a large number of migrants from Europe, while a concurrent frontier culture provided an outlet for geographic expansion, also fueling economic expansion. But while the rest of the world has largely continued growing, and some countries (typically in Asia) that started the 20th with a much weaker industrial base have greatly surpassed Argentina, numerous historians, economists, and political scientists have looked to explain Argentina's stagnation. I do not believe a definitive reason has been found. Certainly, the unique experience of the 1930s and 1940s in the Southern Hemisphere influenced economic thought in ways that would later prove harmful, however the experiences of populism and military dictatorship also took their toll.

Kathryn Sikkink at Harvard’s Kennedy School of Government, in her 1991 book Developmentalism in Brazil and Argentina, examines how certain political ideas that took hold at the highest levels of government in South America's two largest countries, Argentina and Brazil, would go on to influence economic performance. Importantly, the loss of major trade partners over the course of the Great Depression and Second World War would ingrain a focus on internal economic development and instill a persistent mentality that saw in international commerce become a secondary consideration. So in the 1930s and especially the 1940s, entrepreneurs in Argentina and Brazil begin producing goods that had formerly been imported and focusing less on goods destined for export. When international trade re-opened in the late 1940s, there was no effort to re-align the economy to again become a major exporter. For whatever factors unique to Latin America (forgive my vagueness, I am after all an economic historian and not a historian of Latin American politics) policies were put in place to protect domestic entrepreneurs and limit the presence of foreign firms (typically limited to capital investments or large infrastructure projects) even though there was no outstanding shock to mitigate (like a global depression or war). The dominant school of economic thought, called "Developmentalism," wasn't entirely averse to international trade, but believed that an economy should only be opened up once domestic industries were developed enough to compete on level terms. While this isn't an unsound economic argument, the fundamental problem was that internal demand revealed itself to be insufficient to develop truly internationally competitive industries, even after substantial investment from the public sector.

The presence of capital owners partaking in what economists call rent-seeking behavior certainly influenced political decision makers adopting developmentalist policies; Sikkink affirms that oftentimes, protectionist policies were adopted first and economic justifications found later. This might be a symptom of the characteristics tied to internal political discourse and decision-making in countries like Argentina. But it's also true that within international institutions, like the United Nations Economic Commission for Latin America and the Caribbean (CEPAL) developmentalism found broad consensus: most economic growth in Latin America had been fueled by exporting raw materials, and the "traditional" marks of a successful industrialized economy were absent, prompting a belief that promoting industrialization was necessary (as an aside, in later decades some Middle Eastern countries also exporting raw materials would, perhaps learning from the experiences of the developmentalists of the 1940s and 1950s, bypass the "industrialization" phase and instead focus on developing the service sector).

But the "Developmentalists" aren't entirely to blame for economic stagnation in Argentina and Brazil. Economic historians like Jeffrey Freiden at Harvard generally agree that as late as the early 1970s, Latin American economies were under many metrics comparable to much of Western Europe. So Latin American policymakers of the 1950s might have been justified in thinking internal consumption could drive growth instead of exports; thus limiting openness exclusively to the financial services industry (it could be argued that post-1970s European economic growth born out of the opposite policy —regional integration— was more driven by fear of war, with economics a useful corollary). Political turmoil and isolation (perhaps as a corollary to protectionism) in following decades is also an important factor which not only impacted the ability to implement new policies (leading policymakers to follow developmentalist dogma even when no longer necessary) but also reducing the willingness of foreign investors to back projects in Argentina (lest they be undone or reversed by a military intervention or public revolt).

Political concerns trumped economic concerns (or rather, fed into each other) over the course of Argentina's spiral into military dictatorship. However, recovery might have been hoped for in the late 1980s and early 1990s as the Argentine government transitioned back into a more solid democracy. International accords like the currency board arrangement pegging the Peso's exchange rate to the US Dollar also encouraged new interest in Argentina from international investors. However, by the end of the decade the Argentine government would perform the largest default the world had ever seen up to that point. While the details of this event take place precisely one year after this subreddit's twenty-year rule applies, it might be useful to examine why the Argentine economy did not start growing again once democracy had been re-established.

A conflation of democracy and economic openness has existed in political and academic circles since the 1980s. While it is unclear in what order democracy, economic openness, and access to capital markets influence each other, what is important to point out is that there is a measurable correlation between democratization and access to credit markets in addition to more favorable credit pricing (notably measured in the 2012 “Sovereign Debt and Regime Type: Reconsidering the Democratic Advantage” by Beaulieu, Cox, and Saiegh). Thus Argentina, having recently democratized, in the 1980s found itself rapidly caught up in a global commodities boom. Investments in the developed world had become saturated and returns had become unsatisfactory, so markets began pouring money into commodity-rich economies like Argentina as an antidote. However, both public and private borrowers in Argentina were soon proven unable to service the debt they had taken on (especially after central bank rate hikes in the "West" cut off easy new credit to pay off old credit; as examined together with a multitude of other financial crises in the 2009 book This Time is Different by Harvard scholars Carmen Reinhart and Kenneth Rogoff.). Thus the Argentinean economy had quickly gone from being protectionist to being enormously exposed to foreign financial markets with little time to adjust, the end result being enduring instability.

Other readings you might be interested in (some might be available free)

Albert O. Hirschman. 1968. “The Political Economy of Import-Substituting Industrialization in Latin America” (Hirschman was one of the major thinkers behind of developmentalism)

Werner Baer. 1972. “Import Substitution and Industrialization in Latin America: Experiences and Interpretations”

Jeffrey D. Sachs. 1985. “External Debt and Macroeconomic Performance in Latin America and East Asia”

Sarah Brooks. 2004. “Explaining Capital Account Liberalization in Latin America”