Persistent wi-fi (Wi-Fi when off) - Has anyone noticed?

I've noticed for quite a while that the Wi-Fi is no longer staying on when the screen is turned off, but I've never noticed until some off my push notifications were delayed (sometimes hours!). I've grown accustomed to it on my WP7 given it had cellular data, however given I have an iPod Touch for the iOS ecosystem I'm expecting a level of refinement, although both iOS and WP7 remain on when connected to a power source.

I've visited the Apple Forum, with mixed response, usually users claiming that it must be a problem with my device. So is your iPod Touch 5G/iPhone 5/iPad Mini/iPad 4G or older devices with iOS 6 exhibiting the same issues as mine? This is not an issue that I have not been a prominent issue, so please take the time to replicate the issue

TL;DR - Does you wi-fi turn off when the screen is turned off AND NOT CONNECTED TO A POWER SOURCE?