I can't find any information about whether or not the IP address that Azure App Services gives you to add to your DNS A record for custom domains is a truly fixed IP address.
As far as I can tell you can't use Reserved IP's for App Services.
According to the official documentation here and some of the comments, the IP Address we get is a Virtual IP. Does that mean there is a chance we may need to change the A DNS record in the future to a different IP address, even if we never change the App Service? If so, when might this happen?
from the page you linked to
Note:
The IP address may change if you delete and recreate your web app, or change the web app mode back to free.
This means that as long as you're not on the free tier you will get a static IP, which you will keep unless you change to the free tier or delete your app. - which used to be on the Portal, but I can't seem to find it at the moment! - All of my deployment scripts just ping the *.azurewebsites.net address though, and then add that to DNS