In the form we use most often - A Prayer Book for Australia, 1995, "Second Order" of Holy Communion - the rubrics instruct the congregation to stand at various points, but make no mention of kneeling at all. There is a note saying that "local custom may be followed" with regard to posture. That probably saved a lot of arguments, but also hastened the absence of kneeling...
The 20th canon of the Council of Nicea states that since some persons kneel on Sunday and the days of Pentecost it seems best to the council that prayers should be offered standing to preserve uniformity. It may also have been considered appropriate to stand on the joyous day of the Resurrection. This fact of history is often used by those who disfavor kneeling (probably on any day of the week), and they advocate that they are merely restoring primitive practices with the
a priori assumption that primitive customs are always better or more pure than later ones or that customs in a given culture with its own social and historical circumstances always have the same meaning in another time and culture. Oftentimes when I have heard objections to kneeling, never anyone from my parish mind you, the idea is that kneeling is debasing, not worthy of a self-respecting dignified person. This line of reasoning then has nothing truly to do with the Nicene canon or the proper postures for celebrating the Resurrection: in such a case refusing to kneel has a totally different meaning in our culture than it did in the primitive church, and that is the problem with citing early practice as if that proves what we should now be doing.
The wording of the canon is not actually as strong as it could be, and it is disciplinary, not doctrinal. Numerous early canons are obsolete or otherwise unobserved or given lenient applications even in churches that still hold them in high regard in disciplinary matters such as the Orthodox. And concerning the 20th canon it is significant to note that even in the ancient liturgy of the Holy Qurbana of St. James the priest prostrates or kneels for a part of the liturgy, and this despite the general Eastern practice of forbidding kneeling on Sundays as Nicea recommended.
The fact is that in the Western mind kneeling is naturally associated with reverence. Standing is, too: we stand for the Gospel. But kneeling signals and incites reverence and we associate it with such important acts as communing. Whatever arguments are made for primitive practice, when kneeling is forbidden or discouraged for communion for example, people in general receive the message that it must not be so serious after all.
I have not seen these problems in the Episcopal Church but gather from statements here and elsewhere that in some dioceses there is little traditional liturgy. I have seen it in other theological traditions however. For example in local Catholic parishes those very few who kneel for the Sacrament must kneel on the floor as there are no rails, and it can upset clergy and laity alike. However after numerous complaints to Rome from persons allegedly scolded, reprimanded, denied communion, or even assaulted a clarification was made by the Pope that it is the right of Catholics to kneel. This clarification is still being made known to the public. In my brief time in the Catholic Church it was announced that one should preferably bow before communing ,and sure enough almost everyone began to do so. There are reports that the laity are remarking how much more this impresses on them the significance of receiving Communion. I have also heard that over half or more of a parish will kneel for Communion even if the practice is unfamiliar or not recommended if only altar rails are reintroduced.
In summary, the piety of Western Christians nurtured by long development of liturgical practices over the centuries grants us an intuitive understanding that kneeling for certain prayers and acts signifies something important, and academic arguments cannot change that. And if we really wanted to get back to primitive customs and liturgies we would be in for some serious fasting and very different liturgical norms and rites than what we have in modern practice!