HK replied on my e-mail saying this problem is dispatched to a "higher technical department" and that they tested but did not get any disconnections. I suggested that they run a longer test as these problems might only occur after 10-15 minutes.
In the meantime the number of complaints is growing and HK does not respond well to that. In my case they first suggested i'd upgrade to iOS 6.1.2 (from iOS 6.0) but that clearly didn't help. Also i was asked to test the set in another room. The most hilarious suggestion was given to someone on Amazon where HK suggested they'd keep the volume up as high as possible. Obviously that didn't help.
Testing with an older iOS5 device made it clear to me that this problem only occurs with iOS6, in every incarnation until version 6.1.2.
It might well be that firmware on the Soundsticks can't be upgraded by a consumer but HK themselves can. I would not wait for an iOS update. As JimHdK stated there is nothing wrong with the iOS side of things. HK eventually will have to issue a callback action for this but i'm not going to wait for that. My set is going back to the store. I didn't buy a BT set for cabled use, that stinks.
Problem remains that there are no comparable products to replace it. The sound, the looks, the stereo-effect, the price: they are still unbeatable in my view. Anyone thinking otherwise?