Preserving The Time Patrol

If a time traveler who was in a deleted timeline traveled pastward along that timeline to a time before the moment of change, then he survived the deletion whereas, if he either stopped time traveling or merely traveled futureward within that timeline, then he was deleted with it.

After completing every mission, a Time Patroller should jump to the earliest past before returning home, thus ensuring that s/he is in the current timeline, not a deleted one. The Danellians should establish a base with all their records in the earliest past, continually exchanging message capsules with their far future home era. If a message is not acknowledged, then they know that their home era has been deleted and can take steps to restore it.

Or why not instead relocate their entire civilization to the earliest past when it will be safe from the effects of causality violations?