The JW explanation was that the Lord's Supper replaced Passover, which was an annual celebration. Thus, communion is seen as an annual event. The bit about only the anointed partaking relies on their explanation that there was a cutoff for when souls would be allowed into heaven as opposed to having an Earthly future.
That latter one is even more problematic. If Christ's sacrifice was for everyone, then you would assume everyone must partake. It's a symoblic gesture that signifies acceptance of Christ as one's savior and the only path to a 'good' future. Thus, telling the "unanointed" that they cannot partake makes no sense, especially from a group that claims to reject heirarchical titles because we are all on the same level in god's eyes.