Many people who come to Argentina have far relatives who came to Argentina at the end of the 19th or beginning of the 20th centuries. Some people and institutions work on Jewish genealogy in Argentina and they may be able, for a fee, to help you locate your relatives here. Here are some leads you can follow:
If you know a little Spanish, you may want to start trying to see if you can locate the name of the person in the Argentine White Pages: http://www.paginasblancas.com.ar/. You may be surprised to find the name and their telephone number faster than what you thought it would take!