Last time I left Argentine (in June 2013, via EZE) I was given a very serious lecture when I paid my fine (aka "you will never be allowed back in because you have too many stamps") and then lectured again in the same way as I went through migraciones to the plane.
However, when I came back a month later (again through EZE) I put my passport on the migraciones window without saying a word and it was handed back to me with a new 90 day visa stamped in it, again without saying a word.
Given the hit and miss application of the law here by officials, it is impossible to know in advance what will happen in such situations. What happened to me might not be the same thing as what happens to the next person in the same situation.
Bajo_cero2 has explained the law again and again in this and other threads (I don't know how he has the patience). But what many people want is actually psychological - they want to
feel secure despite knowing that what they are doing (living here on a tourist visa) is legally problematic. My advice is ask yourself:
- Can I stand living with this insecurity every time I want to (or have to) leave the country? If it is wearing you out, start the process of regularising your situation (residency or citizenship). If it is not bothering you, take the risk you will be refused next time.
- What will I do if I am refused admission at the Argentine border? Have a contingency plan. Would you be willing to just go back to where you came from (or get a connection to somewhere else)? If you meet the requirements for citizenship it is possible to call a lawyer from migraciones and have the lawyer insist on your admission to the country while you go through the citizenship process. But don't expect to ring a lawyer you don't know and expect them to respond in a calm, knowledgeable and helpful way while you are in a panic - things don't work that way. Have a contingency plan that is well thought through and your backup agreed.
Personally, I couldn't stand the worry, and since I do live here and am not a tourist, I chose to get citizenship. I had expert help (you know who) and it took a long time. But now I am an Argentine, and glad of it.
La Fleur