Keep something in cache even after flushing the cache from the Drupal back-end (not drush)
For this use case, you might need to consider another storage instead of cache. 

warmer -> cache 

warmer -> storage -> cache

storage could be either key value or entity or any other storage you prefer.Check here if you are not sure which one to pick.

This way, your warmed data always persistent in the system and can be purged only by warmer (crontab). 

When cache clear happen, you can always fallback to storage.