Azure Web App Service has Steady CPU Time Increase

Question

I have what is essentially a flashcard web app, hosted on the free version of Azure and coded in ASP.NET (C#). It is used by a small amount of people (40 or so). As you can see in the graph below, the CPU Time was steady for a while and then steadily started increasing around April 1. The problem is that I am now reaching Azure's 60-minute CPU Time per day limit, causing my app to shut down when it reaches that quota.

I am unaware of ANY changes, either in the code or in the websites configuration, that happened at any time period seen on this chart.

Quick note: The large spikes are expected, and I don't believe they're related to the issue. Long story short, it was the day of a competition where the app was used significantly more than usual. This happens every couple weeks during each competition. I don't believe it's related because it has NEVER been followed by a steady increase shortly after. So the spike is normal; the gradual increase is not.

I have restarted the web service many times. I have redeployed the code. I have turned off many features in the C# code that might increase the CPU Time. I checked the website's request count, and it is actually LOWER after that first spike than before it. Even when there are periods of no requests (or something small like <5 requests per hour), the CPU Time is still high. So this has nothing to do with request count or something like undisposed threads (which would get cleared upon webservice restart anyways).

One last thing: I have also deployed this EXACT same code to another Azure website, which I have used for years as the test website. The test website does NOT have this issue. The test website connects to the same data and everything. The only difference is that it's not what other users use, so the request count is much lower, and it does not gradually increase. This leads me to believe it is not an issue in my C#/ASP.NET code.

My theory is that there is some configuration in Azure that is causing this, but I don't know what. I didn't change anything around the time the CPU Time started increasing, but I don't see what else it could be. Any ideas would be greatly appreciated, as I've been wracking my brain for weeks on this, and it's causing my production site to go down for hours every day.

EDIT: Also, the CPU Usage is NOT high at this time. So while the CPU is supposedly running at long periods of time, it never approaches 100% CPU at any given moment. So this is also NOT an issue of high CPU usage.