I have come across a pattern for my connectivity issue. Ping and Tracert from my SSMS client to the remote server as follows:

H:\>ping XXXsql03 -t

Pinging XXXsql03.ssssss.com [X0.X20.X3.X6] with 32 bytes of...

I've had a chance to digest your info and thank you again. I just wanted to summarize by way of an example and then perhaps pose another question.

select fulltextcatalogproperty...

Thanks for the info. I will review and post when I have some new information. Going on leave today so might be a while.

I'm using Change Tracking with Update Index in Background. BOL describes the logsize as representing:

"Size, in bytes, of the combined set of error logs associated with a Microsoft® Search Service full-text...