The BusinessHours_Salesforce synchronized object pauses automatically. A refresh will update the sync data however the object will pause again eventually. This is a limitation with object because getdeleted() call is not supported for this object. As a result, the sync schedule gets paused due to repeated errors for trying the getdeleted() call and puts the object in state of pause.
If changes are made to the BusinessHours object in your Salesforce Org, then you can manually refresh the BusinessHours_Salesforce object with the understanding that the synchronization will pause again because the object continues to fail on the getDeleted call.
You could also import the BusinessHours object as a report, refer to the Resolution section of the following documentation.
Another option is to export the BusinessHours object details then import to your Marketing Cloud org.
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