I got to the root of this issue on my Mac -- but my solution will not apply to everyone. Still, I'm posting this for the benefit of anyone who's in the same boat.
So, if you use SpamSieve, read on:
For anyone who doesn't know, SpamSieve is a very robust, reliable spam filter that works as a plug-in for Mail.app. I've used it for years, and I'm very happy with it. In short, it works like so:
A rule is created in Mail.app that directs all email to SpamSieve. Using complex algorithms that "learn" over time, SpamSieve analyzes each message, puts spam in a folder called Spam, then passes all "good" messages to your inbox.
The day my email disappeared, there were updates to both Apple Mail and SpamSieve.
Bottom line: Somehow, all of the good mail in my inbox (but just on 1 of my 4 email addresses) got moved to the SpamSieve's Spam folder, giving the impression that my mail had disappeared. I'm not accustomed to getting many "false positives" for spam, so I don't regularly look in the Spam folder. But later that day, I did -- and lo and behold, all of the "missing" mail was sitting there, intact.
I also noticed that after the update to Mail.app (and in fact after installing Mavericks, a couple of weeks prior), some of my Mail rules were either missing or had been disabled.
In all these years, I've never had one problem with SpamSieve, so I'm chalking this up to an anomaly -- likely the fault of Mail.app mucking around with my mail rules. I can't say for sure, but to be clear, I've lost no faith in SpamSieve (nor am I affiliated with its developer, for the record). I just want to make it clear that I'm not disparaging SpamSieve in any way.
I simply moved the good messages out of the Spam folder and back to the inbox, and have not had one problem since. Both Mail and SpamSieve are working normally and happily.
I'm posting this because I spent hours online, that day, seeking a solution -- only to discover that my problem had a fairly simple explanation. In the panic of dealing with "disappearing email," it never occurred to me to look in the Spam folder. So if anyone else has SpamSieve, this may point them in the right direction. :-)