I stopped receiving emails on my Apple ID accounts

Can you send emails from the accounts?

Mail (El Capitan): Mail troubleshooting. https://support.apple.com/guide/mail/troubleshooting-mail35552/mac

Mail (El Capitan): If you can’t receive messages. https://support.apple.com/guide/mail/if-you-cant-receive-emails-mlhlp1138/mac

Mail (El Capitan): If you can’t send messages. https://support.apple.com/guide/mail/if-you-cant-send-emails-mlhlp1129/mac

Mail not sending or receiving messages after updating OS X. http://www.macissues.com/2015/07/06/fix-mail-not-sending-or-receiving-messages-after-updating-os-x/

LummiIsland Said:

"I have two apple IDs They seem to be in conflict with each other. I'm not receiving emails on either one?"

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Apple IDs are Independent:

There should be no conflict. They are their own eMail addresses. Each eMail address is assigned to its own Apple ID. And one Apple ID designated per device.

They are completely different accounts. You cannot combine Apple IDs - so a conflict would never come about.

If eMails are being forwarded from one eMail address to the other, then I could see a conflict being apparent, but not so.