I am working on an azure hosted multi-tenant web application. Azure will provision a VIP address on initial cloud service deployment. The VIP address will not change for the lifetime of the deployment. I will have hundreds to thousands of domains setting up A-records to our multi-tenant application (VIP address).
What I am afraid of somehow losing the VIP. That is a HUGE risk. This would be catastrophic in that hundreds or thousands of customers' sites would be down as they would have to change their A-records/CNAME's to the new VIP address.
I'd like to find a way to buy an IP address and use that IP address as a proxy to the VIP so that if the VIP changed (bad things), then I could simply change the proxy to point to the new VIP. How would one do this?
As all your customers are just pointing an A record to "your" IP address, why not setup an A record in your DNS list customers.company.com and just have all your customers point a CNAME from whatever.them.com to customers.company.com. This way if you ever decide to leave Azure and go to another hosting site your customers don't need to change anything. As soon as their DNS cache expires they'll be pointed to your new IP.
That said, the risk of Microsoft changing that IP address on you is basically zero. Just like any other hosting provider they can't go around changing public IP addresses on people.
You can get a static IP address assigned to you by pretty much any ISP, in much the same way you got one from microsoft azure, but you'll have to trust the provider not to change it just the same (and most will reserve the right to change it with notice to you).
ARIN (or your local RIR) will not typically assign /30 subnets for this purpose because it complicates routing and is inefficient, and in any case you would need to arrange for routing on any block assigned to you, which is not a trivial task.