Repair of multiple partially failed cache nodes is studied in a distributed wireless content caching system, where r out of a total of n cache nodes lose part of their cached data. Broadcast repair of failed cache contents at the network edge is studied; that is, the surviving cache nodes transmit broadcast messages to the failed ones, which are then used, together with the surviving data in their local cache memories, to recover the lost content. The trade-off between the storage capacity and the repair bandwidth is derived. It is shown that utilizing the broadcast nature of the wireless medium and the surviving cache contents at partially failed nodes significantly reduces the required repair bandwidth per node.