After doing a lot of research on the best way to automatically back up data, I found that the easiest way to do this is to schedule a task in the Windows Task Scheduler on an Azure virtual machine that uses AZCopy. AZCopy does the work of moving the table data to the virtual machine, and then returns to the second blob store in Azure to store the backup. The batch file also forces AZCopy to copy drops from the source vault account directly to the target account.
You can see a detailed description of how I did this work complete with links to batch files that I use to automate backups using this link: http://www.eastfive.com/2016/03/01/automated-backup -of-azure-storage-tables-and-blobs /
08/02/2018 updating this answer: I raised this question to Azure support on January 18, 2018, believing that they have the opportunity to do it now through a service in Azure. Unfortunately, this is not so, and there is (according to Microsoft support) a better way to backup tables than those that existed when this question was first asked. This is a response from support dated 01.24.2012:
"I reviewed your case and, unfortunately, there is no way to take a snapshot of the entire account or container, and thus, the only way to take pictures using Azure Storage is through iterating the blob and applying the snapshots, and then transferring the bindings to the secondary Account. Or you can just copying the actual files to another account but this will have a higher latency and be more expensive when storing capacity, where the pictures will take up less and be faster transfer.
The methods that we support for the transfer are AzCopy and the Data Movement Library, which can be used to perform custom migration of solutions in Java or C #.
If you want to automate these processes, you can do it through Powershell and Azure Automation or using the Azure functions, but help with these solutions will most likely be needed through another support request, because my team purely supports Azure Storage. "
Thus, there are no automatic ways to perform these backups. My team is working on a library for backups. When we finish, I will post here.