Hi Mike Dynes,
Please check if the VM currently showing as "Running" in the Azure Portal.
If there are any recent reboots, redeployments, or configuration changes to the VM, check them if they are supported or not.
If you are seeing any specific error messages, when trying to connect, please let me know.
Go to Networking blade of the VM: Ensure inbound rule for port 3389 is present (priority number lower than Deny rules). Make sure there is no NSG deny rule overriding the RDP allow rule.
Check the VM Agent status, if it is Not Ready, reinstall the VM agent.