How can I keep an app open in the background? As I was using an app on my iPhone, I accidentally hit the home button. I quickly reopened the app. But instead of it resuming where I left off, the app had to load all over again. (This was Clash of Clans and I was in a raid!)

Is there a way to keep an app open in the background?

Such a feature would also allow me to quickly check something and then return to the app that I was on.
Apps are paused when backgrounded and resume when opened. If an app does not correctly resume to the state it was left in, this is something only the developer can fix.

It's not possible to run an app in the background as if it was in the foreground. Apps can only run a limited set of tasks in the background for a short period of time per Apple guidelines, or use structured backgrounding such as Background App Refresh.

Also see iOS 7 seems to be killing apps too often.