The syncing process usually stops when the API key is expired. When the admin who has generated the API key is terminated in BambooHR, the API key automatically gets expired. Hence, to fix this any of the active site admins need to generate a new API key to reinitiate the syncing process.
Please connect with Engagedly Support <support@engagedly.freshdesk.com> so that they can help you out on generating the API key and initiating the syncing process.