Argentina didn't collapse. It just didn't grow. Argentina experienced strong growth from the 1870s to the 1930s, and then growth stagnated.

Originally, the success of Argentina (and its neighbor, Uruguay - proving that Argentina was not unique) was due to exceptionally rich agricultural lands which attracted immigration (Argentina had the highest percentage of immigrants in the population among all countries at the turn of the 20th century). However, education levels were low (5 years on average completed in 1960, compared to 7 on average for developed countries) and savings rates were low as well.

Savings rates are often cited as the single most effective predictor for long-term growth, with nations such as Singapore, Taiwan, South Korea, and Japan leading the world in the post-war decades in both long-term growth and savings rates, later joined by China. Savings allow for lower interest rates and more domestic investment in an economy. Argentina was able to finance investment in spite of low savings rates by soliciting foreign investment until the Great Depression. After the depression, this flow dried up.

Also as a result of the depression, protectionist barriers increased world-wide. The Argentine economy was dependent on agricultural exports, especially wheat and grain. In 1919-1925, grain prices around the world collapsed as a result of millions of soldiers returning to their farms. To make matters worse, the Great Depression resulted in wealthy countries throwing up trade barriers over their own territories and their colonies and spheres of influence.

In the 1930s-1960s, government attempted numerous times to industrialize Argentina and change the economic model, most notably the cabinets of Peron and Frondizi. Peron established a harsh protectionist environment, isolating Argentine industry from competition but also preventing domestic industries from acquiring cheaply foreign substitute parts. This resulted in a shortage of electricity and steel by the end of his government. Peron also enacted sweeping labor protections and bonuses, which weakened industrial profits and unionized the country to the point where more than 4 in 10 Argentines were unionized. This was similar to the post-war proportion of the USA, but Argentina was a far less industrialized country. Finally, the Peronist industrialization policies preferred flash over substance, with railroad subsidies costing the government upwards of a million dollars a day. Railroads were a particular fascination of Peron, and his government spent 1.7 billion in the day's money to nationalize the railroads, before expanding them and adding numerous unprofitable lines.

These developments have led many to blame Peron for the misfortune of Argentina, but the counter-example of Frondizi deflates this point somewhat. In the eyes of most economic historians, the Frondizi government was enormously effective. Shock therapy and targeted industrial development, aimed at reducing shortages, were effective in stabilizing public finances and the industrial supply situation.

However, Argentina's long-term growth path did not improve at all, in spite of Frondizi's particular brand of pragmatic protectionism being maintained throughout the 1960s.

This is symptomatic of a greater problem. In 2005, nearly 50% of German industries were producing sophisticated and complex goods, compared to less than a quarter of Argentine industries. Argentina never caught up to Europe and America in human capital and education terms. Without a cheap labor pool like East Asia, and without high education levels like the US and Western Europe, Argentine industrialization was stillborn.

Argentina thus remained trapped in an agricultural production model long after that model had ceased to be profitable and effective. The Green Revolution of the 1960s strangled traditional agricultural production zones like the American West and Pampas, because it made marginal agricultural territories more productive. Lack of savings and human capital development doomed Argentina to a failure to adapt.

Sources:

Adelman, J. Frontier development: land, labor, and capital on wheatlands of Argentina and Canada, 1890–1914

Sokoloff and Engermann. History lessons: institutions, factors endowments, and paths of development in the new world.

Solberg, Carl. The prairies and the pampas: Agrarian policy in Canada and Argentina, 1880–1930.

Taylor, Alan. The Argentina Paradox.

Add on: are there any other countries which experienced a similar situation to Argentina in this regard, or is this unique in the world's economic history?