Sometime in the last couple of weeks, my feed stopped validating. There was a <-- comment message --> at the top of the source code indicating that WP Super Cache did not consider it a valid feed.
Feedburner and Feedvalidator concurred. Those trying to subscribe to my feed were instead prompted to either open or save the RSS+XML file on their local machines.
After deactivating WP Super Cache, the feed now validates and people are able to subscribe again.