I have an Azure service that has been running for a long period of time. It builds a word or powerpoint document based on arguments in the request and returns a uri to the
503 error is simply shows that your application pool was inaccessible, it was intermittent because your application pool is restarting because the lack of resource (processor, memory, etc).
Scale up your instance (Cloud Services or VM) to get more resource for the application pool.
For me the error went away when I set up auto-scaling. I think failover requests were getting routed to my second VM, and the second VM took some time to spin up because it wasn't ready for the activity. Auto-scaling shut down my second VM and the error no longer appears (I'm assuming it will spin up if/when I get enough traffic to use it).
Hope this also helps someone.
Looking at the monitoring on my service told me the processor was never exceeding 6% of usage, so it couldn't be a lack of resource causing these intermittent 503 errors. It's bizarre and I'm afraid I have no explanation for it, but simply redeploying the cloud service to Azure appears to have done the trick. It now works perfectly. The solution has not changed, so I can only imagine that whatever 'reboot' is necessary after deployment, has rectified whatever the problem was. All I can suggest is that you try the same thing if you are getting intermittent 503 errors.
I get this error whenever I create an Azure Function with a storage account in the South Central US. If I use a storage account in a different region the function works.
Try a storage account in a different region than the one you are currently using to see if it resolves your issue.