Formidable Pro not appearing in updates available

Problem

Intermittently, when I look at the available updates (either in the dashboard or with wp-cli), Formidable Pro doesn't appear -- even though Formidable Pro is installed, authorized, etc.

I see only Formidable (the free version), and updating all plugins at once (with wp-cli) does not update Formidable Pro.

Then, after updating Formidable free, Formidable Pro does appear in the list, and does update along with the other plugins when I run the update.

This is behavior is intermittently repeatable.  I can roll back my updates and see the same thing happen again.  I'm rolling back with Git, completely restoring the codebase to the state before the update.

Steps to repeat

1. Install & authorize older versions of Formidable free & Formidable Pro
2. Run wp plugin update --all --dry-run
3. Formidable free appears in the list of available updates, but Formidable Forms Pro does not appear.  Similarly, in the dashboard: Formidable free appears as an available update and Formidable Pro does not.
4. Run wp plugin update --all
5. Formidable free is updated, but Formidable Pro is not.
6. Run wp plugin update --all --dry-run
7. Formidable Pro now appears in the list of available updates, Formidable free does not appear because it was updated in the first pass.  Similarly, in the dashboard: Formidable Pro appears as an available update and Formidable free does not.
8. Run wp plugin update --all
9. Formidable Pro is now updated as expected.

However, this behavior is intermittent.  Sometimes, Formidable Pro appears in the list of updates along with all the other plugins, and does update along with all of the other plugins in the first pass.

What would cause this, and how can I consistently ensure that Formidable Pro will update along with all the other plugins in the first pass?