If you want a game to keep doing stuff in the background while the user is not using it, you don't actually need, and don't actually want, to keep the app live and running in the background. This seems to be a common misconception. All it will do is waste the user's resources/battery.
Instead you can use the suspended/resumed triggers to identify when the app goes to sleep and wakes up, measure how much time passed, and then simulate that much time passing on waking up. This is why Construct doesn't have a "keep awake in background" option - for this type of purpose, it's unnecessary and wasteful.