I wanted to share this issue and workaround for the good of the order. Please be aware that VMware has been notified of this issue and the workaround described below may not be supported by VMware. Please also be aware that there are several other known issues with similar symptoms. If your issue does not match the symptoms described below, then this workaround is likely not for you.
The issue began after upgrading vCenter from 4.1 U2 to U3. The symptoms are:
Microsoft KB2653857 indicates that this is a known issue with SQL Server 2008 R2 prior to SP2 (as of 12/21/2012, SP2 is not supported by VMware), as well as SQL Server 2008 SP3. The issue occurs with JBDC connections when "Force Encryption" is enabled on the SQL Server.
To workaround this issue, perform the following steps:
UPDATE: I have confirmed that Cumulative Update 6 for SQL 2008 R2 SP1 resolves this issue. While there is no public documentation to support this, I've been told by VMware support that CU6 is supported by VMware. To obtain CU6, see KB2653857 link above.