I think this depends on what the original contract stated. If a landlord advertises in dollars, he is within his rights to insist that he be paid only in dollars.
I know that my MIL is currently selling her property and buying another here and all of the transactions related to that are in US dollars - which is the norm (all house prices are listed in dollars here).
Whenever I've had to rent a temporary apartment in dollars I have always asked the owner if it would be ok to pay in pesos according to the exchange rate on the day I pay. I can see why they'd refuse, to be honest, given the enormous queues in casas del cambio and constantly fluctuating rates. I think that until an actual law is in place preventing these dual economies in Argentina (which I doubt will ever happen), there's nothing you can do except for pay the specified rate in the specified currency.