Hi JDallB,
welcome to the Apple (user-to-user) Community!
Re: "Why has our IMAP address been deleted from our email accounts on Apple devices"
We are Apple users, like yourself in the community, so we have no access to your accounts or details to determine the reason in your case. Eg: We do not know which eMail provider you use, and whether you are using the Apple Mail app with your account or not. We do not know which devices or device models are affected, or which iOS or iPad OS versions you are using.
You may or may not need to update your iOS / iPadOS etc. versions to the the latest compatible version ... you could check Settings > General > Software updates to see if updates are waiting.
Restarting your devices can delete temporary files, update recent setting changes, re-establish connections, etc... and often restores order if something is not working as expected.
Eg: How to Restart your iPhone - Apple Support / Restart your iPad - Apple Support
You may need to check with the particular eMail provider whether something has changed.
Eg: For GMail / Yahoo etc., there are "support" or "help" webpages on the provider's website that help keep everyone up-to-date with the latest. You just need to log-in on the website itself for that.
________________________________________
Re: "We cannot enter an inbound IMAP address".
New or changed connections may need to be verified by the eMail provider with an email containing a link or a code, for the security of your account. Also, seems some eMail providers now make their own app available for download and use.
If necessary:
You could always try deleting the account, and re-establish the connection by adding the account again. Eg: Add and remove email accounts on iPhone - Apple Support
More info : iPhone, iPad, or iPod touch : Add an email account - Apple Support
All the best :-)