SQL Server outbound IP address inconsistency in Azure VM

I have this setup:

• Azure VM (B-series)
• Static public IP
• SQL Server running outside of Azure, with IP whitelisting on the firewall set tot he public static IP of the Azure VM
• Two ASP.NET apps that connect to the SQL Server on the same IP but with different usernames/passwords

Expected:

• Both apps can connect to the SQL Server and return data

Actual:

• Only one of them can connect to the SQL Server and return data
• Apps running elsewhere with static whitelisted IPs can connect just fine

This is really wierd! Does Azure sometimes use some other outbound IP address?