Aeronautical ad hoc networks (AANETs) dramatically increase the Internet access rates of aircraft by widening the coverage area thanks to the air-to-air links established. However, the mobility and atmospheric effects on AANETs increase air-to-air link breakages, leading to frequent aircraft replacement and reducing link quality. These broken air-to-air links should be transferred to other aircraft to enable the sustainability of the AANET topology. At that point, the wrong and late transfer decisions of broken links make topology sustainability challenging by reducing packet transfer success and increasing end-to-end latency, respectively. Despite these challenges, to the best of our knowledge, air-to-air link transfers between aircraft in AANETs have not been investigated by any study to enable the topology sustainability. This article proposes to utilize learning vector quantization in three phases - winning cluster selection, intra-clus-ter link determination, and attribute update - to enable the sustainability of AANET topology, which is in the form of aircraft clusters. In winning cluster selection, we consider each cluster in the topology as a pattern. Then we aim to find the best matching cluster of an aircraft observing air-to-air link breakage through pattern classification. Then we take airplanes in a cluster pattern as weight vectors with location and queuing delay attributes to determine the intra-cluster links of newly assigned aircraft. Here, the aircraft is modeled according to a G/G/1 queuing system for delay attribute calculations. Finally, according to the freshly established intra-cluster links, we update weight vectors' attributes using the throughput rate as the learning rate. We simulate the proposed system by utilizing OMNET++ and Weka tools with realistic air traffic data obtained from flight radar databases. In these simulations, we can reduce the end-to-end latency of AANET topology by 25 percent and increase the packet transfer rate by 31 percent compared to the methodologies in the literature.