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David, the only way to retrieve e-mails on AOL that you've deleted is by restoring them from the Trash folder. Any e-mails that have been left for more that 24 hours in the Trash folder or deleted permanently from the Trash folder are unrecoverable. Have you checked for the e-mails in your Trash folder?
Sorry, the Trash folder time limit is 7 days, not 24 hours.
This is the process for recovering from the Trash folder.
Step 1: Using your web browser, go to AOL .com. In the top right corner of the AOL page, click on the envelope icon to go to AOL Mail.
Step 2: Sign in to your AOL account. When signed in, click on the Trash icon located at the left panel. This shall open the contents of your Trash folder.
Step 3: In the Trash folder, you will see all of your deleted emails that is not older than seven (7) days.
Step 4: If you want to recover or restore any of the emails in the list, click on the check box to select the email message.
Step 5: When the deleted emails are selected, click on the Action button above then in the pull down menu, click on "Inbox" under "Move To" group of commands. This action will move the deleted emails that you selected back to the Inbox.