First thing to do would be to check if the DNS records are getting updated properly.
Check a DNS site such as this - http://mxtoolbox.com/DnsLookup.aspx
Second, fix any A record or DNS record issues (you may have re add them or delete them, then add them back).
Third, come back to the custom domains section. Here, by default, there will be your xxx.azurewebsites.com something. Along with that, your custom domain should also be visible. If not, then add it back.
Note, sometimes, you may have to wait almost 1 hour after updating your DNS records for Azure to validate your custom domain. Just remember that.