What if my subscription to CMOS Online lapses? Does it invalidate my style sheets based on The Chicago Manual of Style for PerfectIt?

You must have access to CMOS Online in order to use any PerfectIt style based on The Chicago Manual of Style for PerfectIt. If your subscription to CMOS Online lapses, then you will need to renew before you can access those styles in PerfectIt again. Other users (in your team or elsewhere) that have a valid subscription to CMOS Online will still be able to access the styles you created from it.