We could simply focus on the most recent economic crises, which are similar in nature, but I think it may be helpful to take a longer-term historical perspective. Earlier on, Argentina was something of a rising economic power. Quoting from Wikipedia's "Economic History of Argentina":
During the first three decades of the 20th century, Argentina outgrew Canada and Australia in population, total income, and per capita income. By 1913, Argentina
was the world's 10th wealthiest state per capita. [...] [U]ntil 1962
the Argentine per capita GDP was higher than that of Austria, Italy,
Japan and of its former colonial master, Spain.
The same source points to the key for explaining the decline that followed:
Beginning in the 1930s, however, the Argentine economy deteriorated
notably. The single most important factor in this decline has been
political instability since 1930, when a military junta took power,
ending seven decades of civilian constitutional government. In
macroeconomic terms, Argentina was one of the most stable and
conservative countries until the Great Depression, after which it
turned into one of the most unstable.
In the immediate post-war period, the regime of Juan Perón oversaw a profound transformation in Argentina's economic and political system. This is when the country began to turn from a very open, export-oriented market towards a strategy import substitution, which had a mixed record at best, especially in its aftermath.
The era of import substitution ended in 1976, but at the same time
growing government spending, large wage increases and inefficient
production created a chronic inflation that rose through the 1980s.
The measures enacted during the last dictatorship also contributed to
the huge foreign debt by the late 1980s, which became equivalent to
three-fourths of the GNP.
At certain key moments, notably including the present crisis, Argentina's most severe problem has been it's ability to over-borrow from foreign investors and its inability to repay. The resulting financial crises have magnified underlying weaknesses to make recessions extremely severe. Here is a typical analysis of what this looked like in 1999-2002:
Argentina’s debt ratios (i.e. national debt vs. GDP) rose for at least two reasons. First, primary
fiscal surpluses (government revenues minus expenditures exclusive of
interest payments on the debt) were not large enough to cover interest
payments and also retire some of the outstanding public debt. [...]
Second, export growth (and therefore economic growth) was not
sufficiently robust to improve the country’s ability to meet its debt
obligations and lower debt/GDP ratios.
However, over more recent decades (and this is especially relevant to the current crisis), the IMF and other transnational financial institutions have also played an important role in making Argentina's problems far worse then they might have otherwise been. This is admitted by a former deputy director of the IMF in a recent piece in the The Guardian.