It turns out the culprit was a bad font in the image. I opened the image in Illustrator and converted the font to outlines. That solved the problem! Incidentally, this one image/font problem (this image is used in a couple different manuals) also was causing InDesign to crash when I exported to PDF.
Adobe people, if you read this, it would be great if problematic fonts in images were detected by InDesign, like an error in the preflight panel similar to the linking and font errors currently there. I can't see a way to detect this easily now (how to narrow down which image is a problem when working with 50+ images in a document?) Is there a way that I don't know about?
