IBM has now issued the following bulletin regarding this issue:

IBM Apple iOS 12 Mail, Calendar and Contacts fail to sync if HTTP Basic Authentication is not properly configured - United States

https://www-01.ibm.com/support/docview.wss?uid=ibm10731987&myns=swglotus&mynp=OCSSYRPW&mync=E&cm_sp=swglotus-_-OCSSYRPW-_-E

It might be worth checking this out just in case...

https://www-01.ibm.com/support/docview.wss?uid=ibm10731987

Edit: looks like Ned's update beat me to it... Also Daniel Nashed explains the issue very well here http://blog.nashcom.de/nashcomblog.nsf/dx/support-flash-alert-ios-12-native-mail-app-authentication-issue-with-session-based-authenticaiton.htm

The changes made fixed the problem for our iPhones on iOS 12, but stopped the communication to our Android phones.

I believe they are using the standard mail app on Android.

Any ideas on that?

edit:  Android clients that are using the Traveler app/installation are receiving email.  The user's using the standard email app, are not getting email.  Full disclosure:  I know nothing about Android.

the only supported app on Android is the IBM Verse app. No other mail apps are supported...

https://www-01.ibm.com/support/docview.wss?uid=swg27049546

HTH

We had the same issue and the below is the solution working for me

https://www-01.ibm.com/support/docview.wss?uid=ibm10731987&myns=swglotus&mynp=OCSSYRPW&mync=E&cm_sp=swglotus-_-OCSSYRPW-_-E