The symptoms you described indicate that web farm synchronization is not working properly on your Kentico instance. The thing is the server cache should be automatically flushed on all servers which are part of the web farm (all Azure instances in your case) everytime you make a change on any of the instances.
If that fails to happen, it is most probably caused by a bug and I am afraid there were several of them fixed in Kentico 7 related to web farm synchronization. With that being said, due to this reason I would strongly recommend that you apply the latest hotfix (7.0.103).
Let me know in a response if you still experience the same issues after updating.