Recently I was facing a issue with request time out in a web app in azure app services. It was a synchronous file upload which take more than 4 seconds. (Yes, off-course, synchronous way is not the optimum solution)
I investigated this issue and I found that Azure App services (Web app) has default 230 seconds of timeout. If a request take more than this time it will be a 500 Error. But still this request is allowed to continue in the background in server.
So we should keep this in mind and we should design our applications in a reactive way.
So if you are getting a request timeout in Azure web app this could be the issue.