Change from POP to IMAP
I would first change both the iPad and iPhone to never delete messages and let things ride for a week to ensure all your critical messages are handled.

If you don't mind losing some more messages, you can begin now.


Go to settings app on one device and remove that mail account.
That will delete all the messages on that device so you could lose history or messages with this step.
Set up the mail using IMAP host - Apple has an assistant here to verify things before you do this: https://ssl.apple.com/support/mail-settings-lookup/
If Apple's instructions don't work, you will have to contact your mail provider and get them to tell you the sequence to set up IMAP access for your specific mail account.


Repeat the steps above for the second device. If you just want to fix the "not receiving" you could just set all your POP access points to never delete messages until you empty trash and do the deleting on one device only.

Also, if a device other than your iPad and iPhone is deleting messaged via POP - the steps above alone won't guarantee messages don't still go missing.