This comment came to us from Todd Franzen:

This is not to common of a problem although it can be rectified simply.  Pentair's wiring diagram notes to wire the pump and chlorinator live.  As a safety default, we typically wire the chlorinator onto the load side of the filter relay of the control automation or time-clock. This powers down both devices for safety but keeps the programming on the pump control.  We have had good luck with this configuration.