HIV can be effectively treated and prevented with antiretroviral therapy, but the evolution of drug resistance can cause treatment failure. Antiviral drugs typically target a specific phase of the virus's life cycle, and it is generally assumed that resistance arises from mutations that alter the virus's susceptibility to the direct action of the drug. Here we consider the alternative possibility that a virus population can evolve towards synchronizing its life cycle with the pattern of drug therapy. The periodicity of the drug treatment could then allow for a virus strain whose life cycle length is a multiple of the dosing interval to replicate only when the concentration of the drug is lowest. This process, referred to as ``cryptic resistance'', could allow the virus population to maximize its overall fitness without having to alter drug binding or complete its lifecycle in the drug's presence. We use mathematical models and stochastic simulations to show that life cycle synchronization can indeed be a mechanism of cryptic viral drug resistance. We show this effect is more likely to occur when the variability in both viral life cycle and drug dose timing are low. More generally, we find that in the presence of periodic drug levels, time-averaged calculations of viral fitness do not accurately predict drug levels needed to eradicate infection, even if there is no synchronization. We derive an analytical expression for viral fitness that is sufficient to explain the drug-pattern-dependent survival of strains with any life cycle length. We discuss the implications of these findings for clinically-relevant antiviral strategies for HIV as well as other viruses including hepatitis B and C and influenza.