My phone thinks it's charging

After upgrading my Galaxy Nexus to 4.0.4, it keeps thinking the cable is being plugged in and out all the time. The battery discharges at a normal rate, even though the screen keeps lighting up as a result of the random plug events. I don't think this is a hardware issue, but I've not completely discarded the idea either. Has anyone experienced this? Is this a known issue? Anything I can do about it?