I agree with others who have chimed in that this is a power draw problem.
I have used small keyboards that do not draw excessive power successfully (Vortex Pok3r, KBP V60 mini), but only to a point. iOS will reboot itself with every push notification retrieval cycle when such devices are connected and the USB is in an idle state (i.e., the keyboard is not actively being used). I doubt Apple will ever fix this.
I've started using Bluetooth keyboards instead. I am using the Plum Nano 75 now, and it works flawlessly.