Interesting… How many of us experiencing the disconnections are on WiFi networks that have multiple access points or repeaters on the same SSID?
I have a previous generation Apple Time Capsule on my ground floor, acting as a router and the primary AP. Plus a previous generation AirPort Express upstairs in my lab acting as a signal extender and ethernet bridge (so I can hook ethernet stuff up at my desk). Finally there's a two-generations old AirPort Extreme in the garage acting as a signal extender and ethernet bridge/switch.
I'm wondering if the Spark Core is briefly getting a better signal from one of our other APs (on the same SSID) and trying to associate with it, but failing, because it's tied to a specific AP and not the SSID in general.
I've seen that happen before with some wireless enabled devices before. I can think of one case with a Canon All-in-One; when you setup WiFi from the printer's front panel, it'll give a list of MAC addresses for all the Access Points it can see on whatever SSID you're trying to associate with. Once that's locked it, it will only associate with that AP.
Aside from understanding the technical details of how Smart Config works, I don't know much about the inner workings of the CC3000 (aside from interfacing it to an MCU and whatever else was in the basic datasheet), so I'm not sure if the above theory is applicable, but I thought I'd throw it out there.