Various commercial programmable compute platforms have their processor architecture enhanced with field-programmable gate arrays (FPGAs). In a common usage scenario, an application loads custom processors into the FPGA to speed up application execution compared to processor-only execution. Transient applications, changing application workloads, and limited FPGA capacity have led to a new problem of operating-systemcontrolled dynamic management of the loading of coprocessors into the FPGAs for best overall performance or energy. We define the Dynamic Coprocessor Management problem and provide a mapping to an online optimization problem known as Metrical Task Systems. We introduce a robust heuristic, called the fading cumulative benefit (FCBenefit) heuristic, that outperforms other heuristics, including a previously developed one for MTS. For two distinct application sets, we generate numerous workloads and show that the FCBenefit heuristic provides best results across all considered wo...