Asynchronous adaptive specialization of rank- and shape-generic code for processing immutable (purely functional) multi-dimensional arrays has proven to be an effective technique to reconcile the desire for abstract specifications with the need to achieve reasonably high performance in sequential as well as in automatically parallelized execution. Since concrete rank and shape information is often not available as a matter of fact until application runtime, we likewise postpone the specialization and in turn aggressive optimization of generic functions until application runtime. As a consequence, we use parallel computing facilities to asynchronously and continuously adapt a running application to the structural properties of the data it operates on.A key parameter for the efficiency of asynchronous adaptive specialization is the time it takes from requesting a certain specialization until this specialization effectively becomes available within the running application. We recently proposed a persistence layer to effectively reduce the average waiting time for specialized code to virtually nothing In this paper we revisit the proposed approach in greater detail. We identify a number of critical issues that partly have not been foreseen before. Such issues stem among others from the interplay between function specialization and function overloading as well as the concrete organization of the specialization repository in a persistent file system. We describe the solutions we have adopted for the various issues identified.