Android Kiosk Mode Workarounds?
The scope of your question is just so big. I can write two or three chapters of a book on related topics for different device brands, android firmware versions, Android platforms/device-modes, etc. However, this will then also serve as a good handbook /checklist for hackers to look for loophole left by careless administrators. So, I'd rather not do so.
I think you'd better check logs of your problematic device and servers, and first narrow down the most probable area that cause your problem. Then, it will be easier for everyone to focus in subsequent discussions on the solution.