There are different kind of residencies for those who are here without working: pensionista, rentista, estudiante, etc.
Forget the euphemism of perma-tourist, the real word is fake tourist (pseudo-turista).
According to decree 616/2010 and the immigration act, after the first 6 months, you should apply for a residency.
And let´s be honest, there is not another country where there is so easy to get a legal way to stay as soon as you can regularize your situation any time and you can even get citizenship without legal residency. Here the point is the big mistake of the "visa run", the mistake is to believe that doing it you are legal. After the decree 616/2010 there is not a loophole anymore:
ARTICULO 61.- Cuando se verifique que un extranjero hubiere desnaturalizado los motivos que autorizaron su ingreso al territorio argentino o permaneciera en éste vencido el plazo de permanencia acordado, la DIRECCION NACIONAL DE MIGRACIONES lo intimará a fin de que, en un plazo que no exceda de TREINTA (30) días, se presente a regularizar su situación migratoria debiendo acompañar los documentos necesarios para ello. A tal efecto, se lo notificará por escrito informándole, de un modo comprensible, las consecuencias que le deparará mantenerse en la situación migratoria advertida.
So, if you want to stay in Argentina, just overstay and you pay the fine when you leave.
Or apply for a residency.
Or apply for citizenship.
Regards