CRISPR adaptive immune systems enable bacteria and archaea to efficiently respond to viral pathogens by creating a genomic record of previous encounters. These systems are broadly distributed across prokaryotic taxa, yet are surprisingly absent in a majority of organisms, suggesting that the benefits of adaptive immunity frequently do not outweigh the costs. Here, combining experiments and models, we show that a delayed immune response which allows viruses to transiently redirect cellular resources to reproduction, which we call "immune lag", is extremely costly during viral outbreaks, even to completely immune hosts. Critically, the costs of lag are only revealed by examining the non-equilibrium dynamics of a host-virus system occurring immediately after viral challenge. Lag is a basic parameter of microbial defense, relevant to all intracellular, post-infection antiviral defense systems, that has to-date been largely ignored by theoretical and experimental treatments of host-phage systems.