lots of Mail messages missing


I discover a lot of my email messages have gone missing. Maybe 1/4 of them.

All that is there is this message:

"The message from Pen Helm <---@earthlink.net> concerning “Re: photos” has not been downloaded from the server. You need to take this account online in order to download it."

I am online, and am not using IMAP anyway.

I tried saving my mail directories, blowing away my preferences and the mail directories and reimporting from the saved copy... the messages in question simply do not import.

I'm using Mail 2.1.3 on OS X 10.4.11.

When it says "take this account online", it's telling you that your Mail account is apparently off line (or Mail THINKS it's off line)
Open your Mail app, then go to the "Mailbox" menu, then "Online Status"
Choose your account from that list. If it is showing "Take (your account) Offline", then select that. Let the menu close, then re-enter the same menu, and click "Take (your account) Online".
If your account was already showing Take (your account) Online, then simply choose that.
The point is, your account may have been placed offline inadvertantly, so just click to bring back online - and if it was showing online already, then just toggle it off, then back on.
That should fix you up.
Final step should be to select your account from the Inbox folder, then under the Mailbox menu, choose Rebuild.
If your mailbox is quite large (with thousands of messages) the rebuild process can take a long time. I have one mailbox, belonging to my wife (who won't delete anything), rebuild with over 4,000 messages takes nearly an hour. Mine, which has only 40 or 50 messages, rebuilds in seconds.
I did what you said. The missing/damaged messages disappeared. I restored the mail folder from backup, but they're still gone, because of the rebuilt index. :-(
Quit Mail if it is running.
Go in to your user folder, then to the Library. Open the Mail folder.
Find the file Envelope Index. Drag it to the trash.
If you see any other files there with "envelope" in the name, also drag those to the trash. (There's usually only the one, but you may see others)
After doing that, relaunch Mail. You should be asked if you want to import your messages, and you do. Let that finish (and it can take a while if you have a large amount of messages.

This process is the next step beyond the menu "rebuild", and can fix lots of mail issues, such as the dramatic slowdowns that some folks complain about.
I hope it will help you, too.
I hired a programmer to write me a script, which makes copies from backup of my missing messages. Then I (with difficulty) copied them into my Mail folder. I think most of my mail is recovered.