Floating ice shelves buttress inland ice and curtail grounded-ice discharge. Climate warming causes melting and ultimately breakup of ice shelves, which could escalate ocean-bound ice discharge and thereby sea-level rise. Should ice shelves collapse, it is unclear whether they could recover, even if we meet the goals of the Paris Agreement. Here, we use a numerical ice-sheet model to determine if Petermann Ice Shelf in northwest Greenland can recover from a future breakup. Our experiments suggest that post-breakup recovery of confined ice shelves like Petermann's is unlikely, unless iceberg calving is greatly reduced. Ice discharge from Petermann Glacier also remains up to 40% higher than today, even if the ocean cools below present-day temperatures. If this behaviour is not unique for Petermann, continued near-future ocean warming may push the ice shelves protecting Earth's polar ice sheets into a new retreated high-discharge state which may be exceedingly difficult to recover from.