No, it was Pneumonia, this is directly stated by Mr. Ages:
"Your son has Pneumonia. It's not uncommon, but you CAN die from it!"
There are, however, several more instants throughout the film where it was pointed out that the child was in danger of dying.

While I would appreciate a more NIMH backstory focused adaption or just an adaption that is overall more cohesive I wouldn't trust this classic to the writer of Ice Age 5 regardless of the statement being made. This one, however, happens to validate the notion.

That's just it though, most remakes of book-adapoted films are more faithful than their originals. Tim Burton's 'Charlie and the Chocolate Factory' and 'The Amazing Spiderman' are two examples but a more faithful adaption doesn't always translate well to screen.