High Sierra contacts disappear immediately after creation
Solved

Someone in the Apple community gave solved my problem,
 many thanks (https://discussions.apple.com/message/32765319):

Might be a corrupt .plist.

Do a backup, preferably 2 backups on 2 separate drives.

Quit the application.

Go to Finder and select your user/home folder. With that Finder window as the front window, either select Finder/View/Show View options or go command - J.  When the View options opens, check ’Show Library Folder’. That should make your user library folder visible in your user/home folder.  Select Library. Then go to Preferences/com.apple.AddressBook.plist.  Move the .plist to your desktop.

Restart the computer, open the application, and test. If it works okay, delete the plist from the desktop.

If the application is the same, return the .plist to where you got it from, overwriting the newer one.