Currently, Shifter does not fully support wp-cron.

Once Shifter created your static site the container running WordPress will power down. Since the hosting environment isn't running, features like wp-cron which depend on a server are not available.

We are considering introducing some scheduling abilities to use these feature like wp-cron but they're not in the current roadmap.

If you would find those scheduling features helpful, let us know. Your feedback plays a direct role in what we work on next and the features we roll-out.