After I posted my comment yesterday, I had the same problem with one of my apps. I tried force stopping, restarting, clearing the environment, etc. and nothing worked. Then about an hour later, I got an email notification of a critical issue with the app (usually if an app is not starting up successfully, I will get these email messages within a few minutes). Thinking that this might mean the app platform was able to restart the app now, I tried to restart it and was able to. Not sure if you had a similar experience, but if you haven't tried already, maybe you'll be able to start your app too.
Hmm, we had the same issue on thursday 4 december. May somebody from Mendix could give an explanation. To much of a coincidence.
Try to stop the environment and deploy again. The nightly backup may be running on the environment. This is something that is possible to monitor in the cloud portal. In the worse case the environment could be locked where we would need the cloud team to remove the lock. Also check DB size?