How long will synced content be stored on the device after watching it?

This depends on your Mobile Sync settings for that content.

For example, if you have it set to only sync unwatched content, the item will stay on the device until it has been watched. It will be removed from the device when a new, unwatched item is available to replace it or when it marked as watched. If your sync setting is not based on watched status, then the item will stay on your device until you delete it.

Related Page: Plex Pass > Mobile Sync & Cloud Sync