Question:

After running a Source Subscription to batch update specific fields, such as specialties and focus areas, some records are not getting updated, even though the subscription job completes without any errors.

Answer:

This behavior is working as designed and caused by a misconfiguration of the Source Rankings. The System used in the Source Subscription has a lower source rank than the one used to originally load those values. 
For example, the System which ran to perform a batch load System B has a ranking of 3 but the System which was originally used for loading these values System A has a ranking of 2.

Related Documentation:

Network Online Help: Source rankings