Have used Icloud mail for years with push to Iphones (currently 6S plus on 11.1.1), no problems ever. Now no push feature. Emails push to laptop normally, but phone requires manual checking for email. After hours of support chat and finally escalated to engineers (we tried all fixes listed in this thread, even tried my account on two other phones with older IOS), they said that the recent upgrades do not allow push of email from Icloud accounts.
However, even my other accounts that are set for "automatic fetch" that don't support push (gmail, privateemail.com) do not show in inbox until a manual refresh.
I don't know any other things to try and am basically getting used to manually checking for emails. Pretty frustrating after years of normal use.
Any other suggestions (other than all of the settings changes, restore/set up as new phone, try mail on other phones)?