I've been experiencing this lately. For me, it's when the phone gets down to around 30% or less and it almost always happens when I'm using it and doing something that would require data like sending a message. It seems to happen more if that message has a photo in it or something that would seem on the surface to need more battery to get it done.
The other strange thing is that for the next 10-15 minutes I can't restart the phone if I don't plug it in to a power source. I get the "plug it in" graphic when I try. But then after a while it realizes that battery is in fact not fully drained and starts back up with the previously displayed percentage.
I'm guessing this is something where the battery voltage dips enough during a high draw period and tricks the phone in to thinking it's completely drained and in response shuts itself down.
This is exactly what happens to me when the batteries around 10-20%. If I leave it for 10 minutes it will switch on again and the battery isn't drained, it usually switches off when I try to play music or use the map, but not just navigating the phone. I wonder if the battery does just need replacing though, but strange that I have only noticed this since installing iOS7.
I had this same issue for the first time this past weekend. I was using the phone very heavily outdoors. Battery was just over 30% and I was recording videos. The phone cut off like the battery had died. When I tried to turn it back on, I got the same graphic. 20 minutes later, I turned it on and it was fine.
The other strange thing is that for the next 10-15 minutes I can't restart the phone if I don't plug it in to a power source. I get the "plug it in" graphic when I try. But then after a while it realizes that battery is in fact not fully drained and starts back up with the previously displayed percentage.
I'm guessing this is something where the battery voltage dips enough during a high draw period and tricks the phone in to thinking it's completely drained and in response shuts itself down.