You can go to an office on the first floor of the main customs house in Buenos Aires, and ask them where you can apply for an extension of the permission.
They will give you directions to an office in a bank nearby (sorry, can't remember where it is). In that office, you will have to fill out a form and supply lots of photocopies. The form is basically an application for an extension, and the guy behind the counter will give you a reference number.
The form they give you asks for proof of an extension of your tourist visa to match the extension you request for your vehicle.
After a week or so, you need to go back to the original customs house where they should have your file. They will then stamp your permission papers and you are good to go.
Apparently. I got half way through the process and left the country anyway, but they are friendly people.
Argentine friends told me that I was doing this all wrong, and should be ignoring the bureaucracy and paying the pesos if and when a problem arose. But I'm not Argentine, and didn't like the sound of that....