From Aug 2003 to Jan 2007 I was here without permanent residence status, thus forced to shuttle back and forth (visiting family, getting to see Chile & Uruguay in order to keep that visa up to date). I usually spent about 10 months a year in Argentina and 2 months traveling abroad.
After about 10 trips, an immigration officer in Rosario told me that I could alternate the trips to "the exterior" with a stamp at Migraciones at the nearby Port. So 2 months and three weeks later, I went to that office, where the official affirmed that policy. Then he surprised me by saying, "But why do it? Just pay the fine when you leave--it's only 50 pesos. The cost of the stamp is 100 pesos." I paid the 100 pesos as I just can't bear to break the law. I did the same at least three more times.
In 2005 I married an Argentine citizen. So before that, I always (truthfully) told the immigrations officer at Ezeiza or wherever that the purpose of my visit was to see my my fiance. After that I (truthfully) said I was living with my Argentine husband and still waiting for residency papers (and got them 18 months after submitting the papers).
Now I show that residency letter whenever leaving or entering Argentina, mentioning that I am still awaiting the issue of my DNI by the verrrrrry slow Registro Civil, and the Migraciones officers welcome me back and smile sympathetically (truly my best experiences with bureaucracies here). However, sometimes the airline agents at check in will insist on taking my residency letter to show some invisible supervisor behind the counters, returning with a vague warn me that I could have problems with Migraciones. So far, not one, todo al contrario.
I wish all of you out there the best with your visas, Migraciones, and the Registro Civil, which treats its own citizens so poorly that I never take it personally.