P.S. I've also tried using the legacy unsupported SlingPlayer 2.0 client software (windows) and get the same kind of failure.
P.S. 2 -- All of my above testing is done within my home on the same LAN using wired connections for everything (although wifi sees the same thing).
P.S. 3 -- I've ensured java is installed and working. I have not changed any default settings for enablement of java or activex things.
Solved: Per http://support.slingbox.com/get/KB-5000338.html when using ESET NOD32 antivirus software, one must set up an exception for the local in-network IP# of the Slingbox (e.g., 192.168.xxx.xxx).
What I still don't know is whether access while traveling would still be interrupted, given I don't think the computer has any way to know the local home network IP# so it would still be blocking communication to whatever IP# the ISP network provider assigned the home to.