Award tickets get a stopover for free. But keep in mind that any layover >24 hours is considered a stopover. As long as your EZE-AEP transfer is same day it should be fine. But if you want to spend the night in BUE you will need to take the earliest flight the next morning.
You could do a weeklong stopover in one direction and keep the connection in the other direction under 24 hours. (Sometimes there's an exception for taking the next legal connection even if it's over 24 hours, but I don't think that applies here.)