Argentina has defaulted on their debt numerous times and it looks like they're refusing to implement sensible reforms to improve their economy. So why is the IMF still lending them money rather than letting Argentina go completely bankrupt?
As another answer suggests, the IMF is a bank "of last resort". Countries don't usually like to be told what to do, and the conditions the IMF imposes on loans are often what are regarded as "onerous" in that they require particular reforms of state finances and other practices, such as liberalization of the economy (opening up to trade) which can prove highly politically unpopular.
Banerjee and Dufflo, in "Good Economics for Hard Times" (Ch.3, Penguin Economics 2019) have this to say on the experience in India, for instance:
India was forced to seek help from the International Monetary Fund (IMF), an opportunity the IMF was waiting for. China, the USSR, Eastern Europe, Mexico, and Brazil, among others, had begun to take serious steps toward letting markets decide who should produce what. India at the time was the last of the big holdouts, an economy that continued to adhere to the anti-market ideology fashionable in the 1940s and 1950s.
The deal the IMF offered would change all that. India could have the funds it needed [emphasis mine], but only if it opened its economy to trade. The government had no choice. [...]
Countries that are willing to accept IMF "handouts" don't do so willingly, as there is fine print associated.
But what does the IMF gain? The IMF is not a regular bank. It is both a political tool but also a mechanism to encourage development and world trade, and hopefully stability and wellbeing typically associated with these. This is not very different from investors who throw good money after bad chasing the next unicorn, except here the unicorn is "not becoming Haiti", that is, a next-to-lost cause, and maybe "becoming a valuable trade partner".
Argentina, by the way, is not a small country, either in area, population, or productivity, particularly agricultural. It's wellbeing is important for instance for the stability of global commodities such as cereals.
IMF approved a large chunk ($57 billion) when Marci, a neoliberal, was president. He did do some reforms like float the currency (albeit they use a horribly complicated cap scheme, so there's a black market too). But then the Peronists took power. And there was a drought this summer. It looks like the favorite candidate in the immediately upcoming elections is a libertarian, so IMF is probably factoring all those in when they decided not to cut the deal before the elections. Oh, and China gave some $18 billion directly, so there's that great powers competition at play too, probably.
(I'm also aware that Milei has been called other things besides libertarian, but for economics purposes, which is what matters to the IMF, it seem a reasonable description of what he says he wants to do. Also he came in 2nd in the first round a couple of days ago, but the Guardian still concedes that "A Massa [Peronist] victory is not assured given that many of Bullrich’s right-wing voters may migrate to Milei.")
If you owe the bank $100 that's your problem. If you owe the bank $100 million, that's the bank's problem.
J. Paul Getty
Multiply those numbers by around 500 and you get an idea of the problem. This isn't unlike what happened in Greece's crisis, more money was lent to them to allow them to make their interest payments (but the EU had way more leverage to ensure reforms however).
(note: that 40+B$ is 30+% of the IMF's global outstanding loans)
On August 23rd the government persuaded the imf to release a $7.5bn tranche of its bail-out programme, its only hope of meeting dollar-debt repayments and staving off default. The imf’s reluctance stemmed not from the fact Argentina is broke—lending to such countries is the fund’s purpose—but from the fact that most of the cash Argentina must repay this year is promised to the fund itself. Argentina is a rare country with the imf as its biggest creditor, owing the fund a cool $40bn, roughly a third of its external debt. By providing support, the imf has delayed disaster.
The imf lends to the world’s unstable economies as a “preferred creditor”. If a country only has a little cash, it is the first to be repaid. It never takes a loss during debt restructuring. This lets it and other multilateral institutions, including the World Bank, hand out cheaper rescue packages.
Argentina cannot afford its bills; the imf cannot cut the debt it is owed without forfeiting its status as preferred creditor.
The cost of letting Argentina carry on is high. In the coming months, the imf will have to figure out if the cost of cutting it off is higher.
"No matter who wins after the vote, the IMF should insist that the government either bite the bullet - or otherwise the Fund should pull the plug on its support," said Mark Sobel, a former U.S. representative at the IMF.
"Even if that means huge arrears."
Some IMF executive board members have complained in Argentina-related meetings that the country has received preferential treatment, three sources close to the matter said on condition of anonymity.
The lack of "evenhandedness" has come up with countries such as Zambia, Sri Lanka and Ghana facing strict requirements under IMF-led debt reworks.
... "In some cases, a country will require a follow-on program to resolve its balance of payments problems," said Jay Shambaugh, the U.S. Treasury's undersecretary for international affairs.
"But it cannot be the policy of the IMF to roll over programs, or approve reviews, only to avoid arrears without sound policy reforms in place."
Note: I see this as the primary reason IMF $$$ still goes to this serial debtor. It doesn't mean I necessarily agree with it. I tend to be more hawkish than dovish here. As far as I am concerned, this is good money after bad, rewarding more Peronist stupidity, an opportunity cost to using IMF resources elsewhere and is unfair to other countries that don't get such sweetheart IMF deals. But I would also be very open to solid explanations of why I might be underestimating the large scale risks from pulling the plug.