What I have read so far on the web is that there is no way to add a reserved IP to an existing VM (unless I recreate the VM which I am trying to avoid). However, I have noticed
At Build 2015 they announced this is now possible and VERY easy. Simply open Azure powershell and run this:
New-AzureReservedIP -ReservedIPName "ipname" -Location "West US" -ServiceName "somevm"
If you run this it will reserve an IP named "ipname" and associate it with the already deployed instance "somevm.cloudapp.net"