I found out more about why the WordPress Bad Behavior plugin was blocking updating of my Feedburner RSS feed -- apprently, Google got a bunch of its IP addresses blacklisted in project Honeypot, which Bad Behavior uses as one source of spam data. Here is more:
This is caused by an architectural problem at Google, and will require Google to resolve the issue for the problem to go away permanently. The issue is that, in the case of FeedBurner, Google uses IP addresses which are shared by third parties using Google App Engine, some of which are spammers. The spammers quickly get Google’s IP address blacklisted all over the Internet, and suddenly FeedBurner stops working.
If you are impacted by this issue, you can whitelist the affected IP addresses or the FeedBurner user agent string, or disable Project Honey Pot. Be aware that doing any of these will increase the amount of spam you receive. You should also complain to Google, since this isn’t the first time this has happened, and they seem to have done absolutely nothing about it.