Despite global warming and Arctic sea-ice loss, on average the Antarctic sea-ice extent has not declined since 1979 when satellite data became available. In contrast, climate model simulations tend to exhibit strong negative sea-ice trends for the same period. This Antarctic sea-ice paradox leads to low confidence in 21st-century sea-ice projections. Here we present multi-resolution climate change projections that account for Southern Ocean mesoscale eddies. The high-resolution configuration simulates stable September Antarctic sea-ice extent that is not projected to decline until the mid-21st century. We argue that one reason for this finding is a more realistic ocean circulation that increases the equatorward heat transport response to global warming. As a result, the ocean becomes more efficient at moderating the anthropogenic warming around Antarctica and hence at delaying sea-ice decline. Our study suggests that explicitly simulating Southern Ocean eddies is necessary for providing Antarctic sea-ice projections with higher confidence.