After the show and then again today I continued researching and testing. I had the same problem with Adobe FME and OBS, so that lead me to exonerate those two programs. For awhile I suspected the Microsoft Lifecam because the driver for that doesn't give the user much control over the operation of the webcam. I thought it might be putting out a bad frame rate or something.
After that avenue proved mostly fruitless, I turned my attention to the router settings. I didn't find much there, although I did stumble upon a Cisco/Linksys firmware upgrade which I applied. I checked my NIC driver & found it was up-to-date. Then I found someone with a similar problem who fixed it by using netsh to reset his TCP/IP stack. I tried that and voila! that might have done the trick.
I've been casting now through OBS for 3 1/2 hours with no apparent problems. I suspect FME would also be OK. I might just go with OBS since we know FME isn't really compatible with JTV anymore anyway. So, I'm keeping my fingers crossed that these problems are past and that next week's show will go off without a hitch.
For the record, and for my possible future benefit, the steps I followed were:
1. Windows-Q to search for Command Prompt.
2. Right Click on Command Prompt and select Run as Administrator.
3. At the command prompt, enter netsh int ip reset c:\resetlog.txt
4. Restart the computer.
(By the way, my OS is Windows 8.1.)
That's it!
Update May 28: Unfortunately, "netsh" is not the solution. Now I have discovered that the problem seems to manifest itself only when I have a browser running while I am also casting. That's the reason I didn't discover the problem before Monday's show. I wasn't running a browser while test casting last week. Of course I need the browser for the chat window and to update Weebly during the cast. FF, IE, and Chrome all caused the problem. So, I am continuing to research and test. I will give the next update in a new blog post, hopefully tomorrow. I still have some things I'm trying out. Look for more test casts coming soon!