Can't multitask while streaming video via Safari

Yesterday I was streaming a video via AirPlay in Safari on my iPhone 4S, and at the same time I was able to send messages or use other apps on that same device, while still streaming the video. I even browsed the 9GAG Reader app while still streaming the video to my Apple TV 2, all with the same device.

Today, I once again started to stream a video to Apple TV 2, but this time I cannot even multitask. I wanted to send a message while watching a video but when I switch to the message app, the streaming stops. Also, when I stream the video via Safari now, the moment the iPhone locks itself the streaming stops. This was not the case yesterday, as I am sure it continued streaming even when the phone was locked.

I did not do any changes to my iPhone, nor did I update the iPhone or the Apple TV 2 since yesterday. I absolutely changed nothing at all, yet this annoying interruption of the streaming occurs. My network connection is stable and I am seriously wondering: what causes this?

Are there any workarounds? Is this a known glitch?

My iPhone 4S has software version 6.0 running, the Apple TV 2 has software version 5.1. It got updated last week but this problem didn't occur after the update, it occurred only today.

Any help is greatly appreciated.