I spotted a store called iParts in La Lucila who might help you - http://iparts.com.ar/
On the same street there is another store selling Apple stuff but I can't remember the name and I am out of town.
Googling I found MasStation in barrio norte - http://www.macstation.com.ar/locales.php
And another one in Vicente Lopez who says they are an authorized apple repairing center - http://www.reparaciones-apple.com/
Eduardo is a good technician, with affordable prices, knowledge. His cellphone is 1535548739. his small shop is inside a galeria comercial at Salguero y Charcas, where the shops facing the street are a fruit store and a flower shop. Palermo area.
Im having trouble with mine as well. When I plug it in sometimes it doesnt contact and start charging. I have to flip the plug or wiggle it a little. Went to the apple store in Unicenter and they said they cant work on it if it was bought from abroad. I will probably look into the places mentioned above in Zona Norte..
There's a place called GoFix (www.GoFix.com.ar) that has at least a few locations in BA, for apple products. I know of one on Juncal, right near the intersection of Uruguay, in Recoleta and I think there's one at least in Palermo as well. They seem to be pretty official places. Their website says they fix iPods too.
I went by there about a month ago to see about getting a screen replaced and they seemed very professional. I haven't used them yet, although I will be soon - my sister-in-law dropped her iPhone while visiting her parents and cracked the screen a little(second time it's been cracked).
I'd be careful about just whoever fixing these things. A friend of my sister-in-laws had broken her screen about a year ago and we took it to a place on Lavalle near 9 de Julio. It was cheaper than other places (like GoFix), but it was a little hole-in-the-wall kind of place. About a week after the replacement was done, she realized that there was a band near the top of the screen that would no longer read her touch. GoFix said the problem was either poor installation or a sub-standard screen.