Does Alarmify remain open all the time?

Not all the time, sin technically it is not possible:

We need to be able to work in the background with the app closed (we do it only when open) and According to iOS system they only allows it for its products. For more information you can check this official link here

Anyways, for allowing it work just don't remove it from your background.

How? Do not swipe the app off from the multi-tasking screen Screen shown when you swipe up from the bottom to the top of your screen. If possible, it's best to swipe off other apps than Alarmify.