UNLABELLED: Bacteria and archaea face continual onslaughts of rapidly diversifying viruses and plasmids. Many prokaryotes maintain adaptive immune systems known as clustered regularly interspaced short palindromic repeats (CRISPR) and CRISPR-associated genes (Cas). CRISPR-Cas systems are genomic sensors that serially acquire viral and plasmid DNA fragments (spacers) that are utilized to target and cleave matching viral and plasmid DNA in subsequent genomic invasions, offering critical immunological memory. Only 50% of sequenced bacteria possess CRISPR-Cas immunity, in contrast to over 90% of sequenced archaea. To probe why half of bacteria lack CRISPR-Cas immunity, we combined comparative genomics and mathematical modeling. Analysis of hundreds of diverse prokaryotic genomes shows that CRISPR-Cas systems are substantially more prevalent in thermophiles than in mesophiles. With sequenced bacteria disproportionately mesophilic and sequenced archaea mostly thermophilic, the presence of CRISPR-Cas appears to depend more on environmental temperature than on bacterial-archaeal taxonomy. Mutation rates are typically severalfold higher in mesophilic prokaryotes than in thermophilic prokaryotes. To quantitatively test whether accelerated viral mutation leads microbes to lose CRISPR-Cas systems, we developed a stochastic model of virus-CRISPR coevolution. The model competes CRISPR-Cas-positive (CRISPR-Cas+) prokaryotes against CRISPR-Cas-negative (CRISPR-Cas-) prokaryotes, continually weighing the antiviral benefits conferred by CRISPR-Cas immunity against its fitness costs. Tracking this cost-benefit analysis across parameter space reveals viral mutation rate thresholds beyond which CRISPR-Cas cannot provide sufficient immunity and is purged from host populations. These results offer a simple, testable viral diversity hypothesis to explain why mesophilic bacteria disproportionately lack CRISPR-Cas immunity. More generally, fundamental limits on the adaptability of biological sensors (Lamarckian evolution) are predicted. IMPORTANCE: A remarkable recent discovery in microbiology is that bacteria and archaea possess systems conferring immunological memory and adaptive immunity. Clustered regularly interspaced short palindromic repeats (CRISPR) and CRISPR-associated genes (CRISPR-Cas) are genomic sensors that allow prokaryotes to acquire DNA fragments from invading viruses and plasmids. Providing immunological memory, these stored fragments destroy matching DNA in future viral and plasmid invasions. CRISPR-Cas systems also provide adaptive immunity, keeping up with mutating viruses and plasmids by continually acquiring new DNA fragments. Surprisingly, less than 50% of mesophilic bacteria, in contrast to almost 90% of thermophilic bacteria and Archaea, maintain CRISPR-Cas immunity. Using mathematical modeling, we probe this dichotomy, showing how increased viral mutation rates can explain the reduced prevalence of CRISPR-Cas systems in mesophiles. Rapidly mutating viruses outrun CRISPR-Cas immune systems, likely decreasing their prevalence in bacterial populations. Thus, viral adaptability may select against, rather than for, immune adaptability in prokaryotes.