No, I'm sorry, I did not. I was in a rush to fix the issue, and simply turned it off.
Aaron D. Campbell, in point 2 of a previous comment in this thread said "2. Your server is limiting loopback calls. This basically means that your server is keeping your site from calling itself.".
I called the hosting company, GoDaddy, to find out what their limit was. 10 hits per minute, that is, once per 6 seconds.
I then reasoned that it's possible that BWPS might be limiting that, or, perhaps that TWP might attempting to access a file that is either (for some unknown reason) blocked or limited by BWPS.
As soon as I turned it off, her twitter feed updated. Since it solved the problem, and I have a reasonable amount of trust for the GoDaddy network, I left it off.
However, should Mr. Campbell discern a cause, based on these further observations and speculations, I'd like to know. I consider BWPS to be essential in most of my installs, and I might use TWP on another install at some point.