Depending on where you are in the city, this rule varies; however, generally most places are closed on Sundays or close early. We live in a hostel in San Nicolas, which is the financial district of Buenos Aires, and come Sundays, everything in our neighborhood is closed. If we want to go out to eat or go to a cafe we usually need to walk about 20 minutes to either San Telmo or Recoleta where things are more likely to be open.
You can almost always count on places in San Telmo being open on Sundays because of the Sunday market on Defensa street, and places in Recoleta near the cemetery are most likely open as well due to tourism and the market that is there on the weekends. But regardless, it can be extremely hard to find places to go on Sundays. If you are aware of this upon coming to Buenos Aires, it is really not difficult to deal with, which is why we are writing about it, but if you come to the city without knowing it, like Kellianne did, it can be a bit frustrating at first. So just remember the Sunday rule and you will be fine!