Q: Will the virtual IP address of my Windows Azure cloud service ever change?
A: When a cloud service is created and has at least one resource running within it, a virtual IP address (VIP) is assigned. The VIP is the IP address the cloud service is accessible as from the Internet—and therefore accessible to resources within the cloud service via defined endpoints. The VIP assigned to the cloud service never changes as long as the cloud server contains at least one provisioned resource (i.e., a resource such as an IaaS virtual machine that isn't deprovisioned—which means you're still paying for it). If every resource in a cloud service becomes deprovisioned, then the cloud service effectively becomes deprovisioned and loses its VIP. A new VIP must be allocated when a resource is reprovisioned in the cloud service.
If you want to ensure that your cloud service keeps the same VIP, you need to ensure there's always at least one resource provisioned. One cheap option is to create an extra small (xs) virtual machine and leave it provisioned at all times. At current pricing, this would cost approximately $15 per month and would ensure that your VIP never changes.