My two light sets had the same issue - half of each not working. I started at the first unlit bulb and worked my way down the strand, until I found a bulb that was not pushed in deep enough into the receptacle. At another location, the unlit bulb was pushed in enough, but the tiny copper strands on the base of the bulb were broken. I replaced it with a new bulb and the whole strand worked fine.
On another set of lights, one of the two wires that go into the receptacle had pulled loose from the receptacle, so there was no connection. I just snipped the light out of the circuit and spliced the two wires together, with success.