How to keep an app running? I have installed a talking clock app (named "Tell Me The Time") that say the current time every quarter hour. However I does not stay active and I have reopen it occasionally. At the same time, another similar app does not have this issue and remain active in the background. How to keep an app active (running) in the background (24/7)?

The issue is also more serious in using Torrent clients (they actually are useless in android).
It depends on how the app has been developed. Generally, android service needs to be running if you want the application to remain active in the background. But, if services are not used, then as soon as the activity disappears or destroys, behaviour is no longer observed.