I noticed that one of my feeds* wasn't updating and checking NewsBlur's handy error page showed that there was a HTTP 503 error. Visiting the site resulted in a CloudFlare JavaScript check which suggested that was the cause of the problem. I created a FeedBurner feed from the site's original feed and added it to NewsBlur which solved the problem.

Perhaps this will be useful to others who might experience the same problem.

* Jonathan Zdziarski's blog (http://www.zdziarski.com/blog/). I created http://feeds.feedburner.com/ZdziarskisBlogOfThings and added that to NewsBlur