It might not look like a regular strand of lights, but it acts just like one of the longer strings of lights, that half will go out at a time if a bulb blows. The wires just might not be tangled as nicely.
My guess if that if you checked all of the bulbs, there is a bad contact between one of the bulbs and the sockets.
I've used a light keeper pro to find the problem on some of the old wire frame figured that have had similar problems.