To keep your access clean you must comply to the law and immigration law. A tourist cannot spend more than 180 days a year in the country that is clear. I understand that enforcing this is not nice for some, but I believe you do not go breaking the law and playing games in your home countries if you are coming from the so called first world - USA, EU, Australia, Canada, etc. I have read for years complaints about the third world thing, and this and that and how laws are not enforced, etc and now all of a sudden its wrong to do it? To top it off, I have read in this post comments about how they bug good people spending money here and not going after other immigrants, etc when in fact Argentina has treaties with Mercosur countries, just like EU has treaties and the USA. In the eyes of immigration officers, a person from EU, USA, Africa, Irak, Honduras, Russia, get the same treatment.
Ok, now that you hate me for the way I think, I add that I believe if in any of the bordering countries is easier for you to get perm residency, like somebody mentioned Paraguay, you should go for it. Being a perm resident in any Mercosur country will be the key to staying in Arg as long as you want. That if you are unable to get any kind of visa here or if you are not willing to try to get Arg citizenship.
I suspect that if this sudden enforcement is true, it might be linked to the whole dollar bill issue, as I had read a while ago that the new controls for people buying air tickets and touristic packages in Argentina were implemented because many tourists were abusing it, hence they were giving away too many dollars at the official rate to tourists taking advantage of the blue rate, etc.
Another possibility is that they are planning to give some kind of amnesty, like NK did with the Patria Grande plan to all perma tourists.
Anyway, staying in a foreign country taking advantage of a loophole, could be fun, easier, etc, but you have to know your risks, and I guess this is one of them. I truly hope that whomever is affected can get it sorted out the best way possible.