Just to elaborate on the dual-band problem: Many dual-band 2.4 and 5 GHz routers try really hard to move traffic to the faster 5 GHz band (Apple routers seem to be a particular problem) so the symptom is usually that your devices can connect for some time and them suddenly they are disconnected and need to be reset to connect again.
This sounds just like your problem except that your problem happens a lot faster (2-10 seconds you said) than most other cases I have seen. Changing the SSID of the 5 GHz band temporarily makes it impossible for the router to try to move devices to the high band and proves what the problem is. You would then want to look for a router setting that prevents moving connections to the higher band as a more permanent solution. Juniper calls this switching to the high band “band steering” so you can check the settings for your particular model.
In my opinion, until you eliminate the 5 GHz band problem as “the problem”, there is no point in trying anything else.
For an AP mode device, the BSSID is just the MAC address of the base station. It is broadcast in every beacon packet and used in almost every packet. I know that wiced does give the BSSID when you do a scan for all WiFi networks, but I don’t think that is returned to user level today. I am not sure how that could help you in this case.