You'd probably want to look into something like Background Manager. It allows for you to keep processes running in the background even though they normally quit when you either close the app itself or when you lock your device. Just note that if you use it for data fetching apps like online games, Facebook (even though it does it by default) and the like, it will drain your battery. It has a whitelisting option that allows you to selectively choose what you want to be affected by Background Manager, so if you choose the Grooveshark app for example, it will only keep Grooveshark open (along with whatever's currently running by default on the iOS).
I've been using it since iOS 6 on all my devices and it works like a saint.