Core issue
This problem occurs due to the presence of the bug CSCsd64333.
When this problem happens, the Domain Name System (DNS) cannot be resolved to internal hosts through the Secure Socket Layer [SSL] VPN Client (SVC) adapter. The DNS requests either seem to go to the wrong adapter or they do not occur at all. However, the routing table appears fine on the SVC client.
It seems that a restart of the physical adapter, either a disable or enable, could be the cause of the problem.
Resolution
For a workaround,
Download and Install the latest SVC client package, sslclient-win-1.1.1.164.pkg.