If a 1.2 update "solves" this problem, it will because they have removed the 1.1 "Feature" of "No Headset Pause".
There still seems to be some confusion on this, so let me share all that I have learned from talking to the folks at Apple.
When the Nano 6th Gen was released, there were lots of folks complaining that they would put it down for the night and when they got up in the morning, the battery was dead. The main reason for this was that they were putting down their unit after removing their headset, not realising that the Nano was still playing music, or the radio or some other content.
So the folks at Apple decided to help users preserve their battery life by putting a feature into the 1.1 update that would pause playback if at certain times, no headset was detected.
There are two times (that I know of) when a Nano will check to see if it has a headset connected. One is if you hit the sleep/wake button one time quickly. This turns off the screen and tells the Nano to go off and check for a headset. If it does not find one, it will pause your playback.
The other time is 60 seconds after you have left the Nano idle but playing. At 30 seconds, the screen will dim then at 60 seconds the screen will turn off completely. If it does not detect a headset at that time, it will pause playback.
I happen to have a friend who is a dentist. He had this happen to his Nano. He took the following picture of the inside of his headset jack using one of the cameras he uses in dentistry:
The interesting thing to note about this picture is that the inside of a headset jack is all white. All that dark stuff is crud. Now the pin that detects whether or not a headset is connected is buried under that dark crud. Once he cleaned it out, his Nano stopped pausing when the screen turned off.
Here is a picture he took of the inside of my Nanos headset jack:
You can see quite a difference. That silver bit at the top edge of the bottom is what your headset jack needs to be touching for it to be detected by the Nano. If there is anything between your headset jack and that bit, your Nano will pause when the screen turns off or when you hit the sleep wake button.
The only other thing that could cause your Nano to pause would be if that pin at the bottom is damaged/missing/abducted/broken/disconnected/etc.
That is the long and short of it. If the inside of your headset jack looks as clean as picture 2 and you are getting pausing - you should take your nano back to the Apple store or call Apple support. However, the odds are that you have lint, mud, ear wax, cheese, sand, confetti or some other random crud stuck in there that is causing your problem. Or - you are just not pushing the headset in far enough.
The only other thing to take from all this is that you should think about where you keep your nano when it does not have a headset jack plugged into it. Pockets, purses, backpacks or all those little places to shove it in your car are likely to leave it vulnerable to all kinds of crazy junk finding its way into the headset jack and screwing up your ability to play music without pausing.
Hope this has helped.
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