Honey bees usually do not succumb to varroa mite infestations. Rather the mites are carriers of the deformed wing virus (DFW) and transfer the virus to the bees. When the infection level becomes too high the hive/colony expires. This usually occurs in winter do the virus having a longer time to replicate in the longer lived winter bees. The attached article is for those beekeepers with a scientific background and discusses the how DFW does its damage to the colony.
So maybe we just need a vaccine for DFW. I wonder whether you would give the vaccine (if one existed) to the bees or the mites?