It depends on if you are exempt a visa or not
An interesting question as I have entered and left Argentina multiple times over the past 2 years. I always was given a 90 day visa and assumed that the clock started anew with each entry. Below is a link to the Argentine Consulate General in UK. You can see that if you are not exempt a visa you get 90 days regardless of if you come and go -the days are cumulative. A 90 day extension is possible. If you don't require a visa (my case New Zealand passport) then each entry you get 90 days with no set rules as to how many times you can come and go except that if the authorities consider you are abusing the immigration process they can limit you entry at their discretion.
https://clond.cancilleria.gob.ar/en/node/2433
I didn't research the situation for Chile but I have entered and left Chile many times and always got 90 days with never any suggestion the days were cumulative in a year
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