Teo Lachev notes that you can process Azure Analysis Services cubes without maintaining an HTTP connection:
AAS supports processing tasks asynchronously with REST APIs. The difference is that the service component (REST API) maintains the connectivity to the server – thus reducing the chances of HTTP disconnections from the external application. Microsoft has provided a RestAPISample console app to help you get started. As with any REST API invocation, you’d need to register the app in the Azure Portal so that you can authenticate successfully. Other than that, it’s simple to invoke the REST API and Microsoft has provided step-by-step instructions.
Another, although synchronous, option is to run a PowerShell script in the Azure Cloud Shell environment. You can upload the script as a file. The script can ask you to provide credentials interactively (Get-Credentials method) or you can hardcode the credentials. Here is an example of a PowerShell script that processes a specific table.
Click through to check out how to do this.