I am guessing you ave unsubscribed folders, such as a spam folder. Right click the account in the folder pane and select subscribe. Make sure all the folders for the account are selected.

That was a good thought and I appreciate your response but, unfortunately, it didn't correct the problem. To double-check, I sent another test message to that account and the same thing happened again: the notification of a new message appears (with the unread message count incremented by one), the account name turns blue, no messages are displayed.

I've tried deleting and re-adding the account and all the suggestions I could find in the forum about similar problems, to no effect. I'm baffled.

tried repair? Right click the folder, select properties and then the repair button?

Yup. Tried that, too. I feel I'm missing something obvious. It's the only account of four with that issue. Two other addresses are POP and share a domain, this one is IMAP and shares a domain with one other which is functioning normally. All the settings between the two are identical, but for the obvious account-specific details such as address. The weird thing is that TBird knows it's getting the messages, apparently, but just won't display them.

do you have that account also displaying mail on a phone or tablet? Just wondering if they get removed right after arrival as the phone downloads and removes them from the server.

Nope. Right now, the only email client running is this instance of TBird. Meanwhile, the notification keeps chiming away about the unread messages. Fortunately, it's my least used email account.

I really appreciate your taking the time to think about this.

what happens when you click the message saying you have the message?

If I simultaneously send to both the email accounts on that domain, when the popup with the Thunderbird logo appears, it displays the incoming email for the one account which has always worked normally, not the other defective account. For that defective account, the account name turns blue in the left-hand panel but--again, no messages appear in the inbox and when the inbox is clicked no messages appear in the right-hand panel. I am on the point of giving up and switching email clients.

Incidentally, the small Thunderbird incoming email icon in the taskbar Notification Area also shows that the defective account has incoming messages. The problem remains that none of these messages is displayed in either the Inbox folder in the Folders or Message panes.