I'm not sure if this is the answer, but I've had similar problems.
Try to replicate this with the third party adapters.
1. Play music on the Nano through headphones.
2. Stop playing the music (ie. turn off the iPod).
3. Take the headphones out of the jack.
Now try on the third party adapters. If I'm correct, the Nano WON'T play.
Now try this:
1. Play music on the Nano through headphones.
2. Pull the headphone jack out of the Nano.
Now try the third party adapters. If I'm correct, the Nano WILL play.
I was traveling yesterday/today, and tried to plug the Nano into my travel speakers in the hotel. Didn't work.
So I used the mini-jack plug (for 2g iPods). That worked. I used the Nano for my alarm clock this morning. Before I left the hotel room, I wanted to give the Nano a quick charge, so I unplugged the mini-jack connector while music was playing and plugged it into the speakers. I had music. I was confused.
I arrived back at the airport and (after listening to music on the plane), unplugged my headphones from the iPod, while the iPod was stopped and off. Plugged it into my car adapter (made by Dension), and it wouldn't work. Perplexed, it hit me--given the location of the dock connector and the mini-jack, Apple must have figured that they can save energy by ONLY playing music through the dock or the mini-jack, BUT NOT BOTH AT THE SAME TIME.
So, I plugged my headphones in, hit play, pulled them out without stopping the music and then plugged into my IceLink. Sound.
Could it be that the Nano switches back and forth based on an order of events?
I just plugged my Nano into an Apple dock--the Nano registered a sound (the "I'm plugged in" sound, and played). Is there something different with the Apple docks compared to 3rd party docks?
Anyway, that's my theory--can anyone test and let me know if I'm right, or if I'm crazy?