Checking the box under Options -> Reading that says “WordPress should compress articles (gzip) if browsers ask for them”. I had it unchecked to make my Global Translator plug-in work – which it hasn’t since two months ago.
I finally figured out when something told me to check for an error message in the Feed Validator. I hadn’ previously done this, because the error in FeedBurner was always that the feed had a timeout error. I thought it had something to do with our last server upgrade, because it’s been a problem since that day.
And, of course, the Feed Validator gave me a message stating, in essence, that my site was telling the browsers that the feed was compressed when it wasn’t. Which fixed the error, and explained why I could see the raw feed in my browser and in some feed readers, but not all of them.
Yay Feed Validator! And welcome back Feed Burner subscribers and feed access points!
Hope this helps someone else… 
I’m reasonably smart and a bit of a techie and I was baffled.
