Question:

Is there a limit to the number of errors seen In the Refresh Administration Section of the CRM Approved Email Integration Page?

Answer:

The Approved Email Integration runs in batch sizes of 200. If there are errors encountered during a batch the integration completes for the current batch but no other batches are processed.

If you see that the rows processed value is near 200 and there are errors present, there could be additional batches that were not processed. 

The solution would be to resolve the visible issue to allow another batch to process.

Related Documentation:

CRM Help Documentation: Integrating CRM and Vault for Approved Email