AOL email customer can set up and use their email accounts on all email programs that support IMAP or POP. With the proper AOL email settings, you can set up your AOL email account in email clients such as Microsoft Outlook, Aol mail server settings, Thunderbird, Outlook Express, Apple Mail, Eudora, Foxmail, etc. IMAP or POP are different mail protocol's that allow you to access, view & download emails from a mail server to mail client. these days, IMAP is the more common option. It keeps your email (& folders) on the remote email server. IMAP also allows you to use multiple devices, including phones, to access the mail server and keep all devices synced with the mail server.

Why are my AOL mail disappearing automatically?

You have enabled the forwarding settings on your AOL account.

Email filters are moving those emails into the other folder.

An anonymous person has deleted the emails.

Your device or app is unable to sync with the AOL mail server.

These are the four most common reasons for AOL mail disappeared issue.

How To Fix AOL Missing Emails Problem-

Let’s login to your AOL account using the net browser. If you can’t access the AOL mail account, Go to Fix AOL mail login problem

Click on the settings & select the mail settings.

Under the filters section, you need to select the filters and click on the delete button.

AOL emails disappeared from the iPhone while they're available in the webmails?

If your AOL mails have been disappeared from the iPhone, while they're available in the webmails.

it can be due to the 2 primary reasons:

iPhone is unable to sync with the AOL mail server.

You have configured your account using the pop settings.
In a easy way, you should try to delete the account on iPhone, and re-add it using the auto settings or IMAP settings.