To start with, if it's the only app in the kiosk and you want to be certain it keeps running its tasks, you should use single app mode to ensure the app is always open or alternatively use a script periodically in a task scheduler to check if the app is in the foreground and if not start (this can be done using JavaScript)

As for the kiosk screen being forced to the foreground periodically, that's unusual. It sounds like your reinstalling the kiosk periodically. It's also possible that it's not the kiosk being pushed to the foreground but Android pushing your app to the background.

There's also some inefficiencies in the way the app runs that I would suggest you look at if it's your app, or check with the app developer. Apps can run tasks even if they arnt open (fully closed) if they are designed to do so.

Is it possible that your device has some aggressive power-saving mode enabled such that idle programs are killed/moved to the background after some time threshold or other criteria are met? If so, simply disabling such mode may leave your app in the foreground and get the problem solved.

Also, Android architecture have been supporting for over 10 years  "background service" software modules that get loaded, and be called called any time to serve other normal "activity" software modules from the same or different app(s).  Your software might need to be modified/rearchitetcted to take advantage of this module type partitioning to solve your current problem.