It is also possible that your customers mail client (ie: Eudora, Netscape Communicator, Outlook etc.) and/or their corporate mail server are using filter device that delete mails off & on with inappropriate wordings (ie: free, $$$, etc.) in your mail: Subject, TO, FROM, as well as message body and will also result in your mails getting deleted.
See Email Filtering

Keep in mind that AOL doesn't show the FROM: name that you provide, it only shows readers the FROM address, so make sure you are not sending with a typical spam like looking email address like this example: jonessnews_1234@myemaildomain.com
that is as good as telling the recipient or the spam filters "you can delete this mail".

From: name?
It is the name that you have enter into your email client ie: Outlook Express, Name: field--(start-up outlook, >Tools, >Accounts, >Properties and at the "User Information" Name: field--that's the From: name that won't show-up for AOL recipients.

If your off & on refers to undeliverable mails

Bounced or undeliverable mails from your own or ISPs mail server are quite normal due to various reason like; Busy mailbox, blocked domain, mailbox full, account temporary suspended, mailbox over limit, etc.--these are know as soft bounce. Therefore, bounced or undeliverable mails off & on does not necessarily mean that your mail address is invalid.

Soft bounced refers to; mailbox full, mail server down, network busy, (550 Requested action not taken) etc.

Hard bounced refers to non-existing users (550 address not allowed or Requested action not taken) or that mail servers or email clients have filtering device that stimulate and return mails as hard bounced. See: SMTP return codes error

Free filtering programs like: www.mailwasher.net let users auto delete and returned undeliverable emails stimulated as hard bounced.

These powerful freeware programs allows *wildcard filtering for the: Subject line, TO, FROM, email domain and message body.

For more info about why your emails are bounced...
See: How Email Works

Important Notes:
If you are using your own mail server program and facing bounced, undeliverable or deleted mails by AOL, Yahoo, Hotmail, etc.
See: Mail Server FAQs