Where's My Old Mail??? (Sorry if it's been asked before)

I've never used AOL mail (and never would) but you might check if they provide an option to use IMAP instead of POP mail. The former keeps your mail on the server and doesn't delete it unless you delete it. If needed you can also have local copies of the mail.

I suspect what you are observing may be due to the way in which your mail account is configured. In Mail you need to check Mailbox Behavior in Mail's accounts preferences to be sure you haven't selected an option to automatically delete mail after a give time period. You should also see how you've got your AOL account configured. AOL may very well delete mail after one month automatically unless otherwise configured.

No, Mail does not do any automatic archiving. Select Preferences from the Mail menu then click on the Accounts icon in the toolbar. Click on the Mailbox Behaviors tab. There are options there for scheduling the deletion of the contents of specific mailboxes. Be sure you have it configured to your preferences. Then click on the Advanced tab. There is a label, "Keep copies of messages for offline viewing." A drop down menu is used to select the option your prefer.

Close the options window (you may be prompted to Save changes) and then click on the Rules icon in the toolbar. Be sure you haven't configured any rules to automatically delete mail.

Other than that I don't know what to suggest. Mail does not delete messages and if the messages are left on the server and not being deleted, then they should all display whenever Mail is opened.

This is an AOL issue. Mail has no bearing on it. You’d have the same problem with any other IMAP mail client. The messages disappear from the server because AOL (not Mail) removes them from there. The messages disappear from Mail (and they would also disappear from any other IMAP mail client) as a result of Mail synchronizing with the server, which is precisely how IMAP works, i.e. you see in the mail client what’s on the server, no more, no less. You cannot blame Mail for doing what an IMAP mail client must do and not handling AOL’s bizarre behavior in a special way...

If you don’t want to lose those messages, you must store them in local “On My Mac” mailboxes in Mail ( not Smart Mailboxes), just like you stored them in the Filing Cabinet when you used the AOL application. Read the relevant articles in Mail Help for more information on how to create custom “On My Mac” mailboxes and organize your mail there however you wish — and you should also read the articles that explain what Smart Mailboxes actually are and how they work.

Oh! And AOL doesn’t let IMAP mail clients such as Mail to create or manage mailboxes at the root level of the account directory on the server, only as subfolders of Saved, which means you should turn OFF Store messages on the server for all the mailboxes in Mail > Preferences > Accounts > Mailbox Behaviors, so that Mail stores those mailboxes locally on your computer instead — yet another example of the incredibly lame AOL’s IMAP access...

I think David has given you a pretty thorough review of the situation. All the more reason for finding an alternative to AOL. If they are your ISP consider not using them for anything other than your internet access. If you can find an alternative ISP I would encourage switching. You'll probably find you have better internet access and speed and none of the limitations AOL imposes. Just be sure you use an ISP that supports IMAP mail accounts.

Actually I've never used AOL. I've been using OS X 10.4 for 2.5 years (now 10.4.11) and use Mail 2.1.3. I just noticed that my saved mail messages are disappearing after one year, rather than one month as mentioned by previous questioner. It makes me think there must be a variable flag, only I can't find it.
In Preferences/Accounts/Mailbox Behavior, the only mailboxes I can se to never delete mail are the Sent Box and The Junk Box...both of which I have set to Never. And yet all boxes, including Sent And Junk, contain nothing older than one year.
Its very disturbing to loose mail. Any further thoughts? I've looked pretty hard and can't find any setting to alter. A the risk of heresy, Apple does not make it easy to learn how to use their product.

Mail doesn't do this. It's more than likely something being done at your ISP or wherever your mail account is.

Apple makes it very easy to learn. You received a user manual for both the computer and OS X. You have online help available by just selecting from the Help menu of any application. Apple has online tutorials via their website. You just need to take advantage of these.