There seems to be much confusion about this, so I am glad that FatherHLL has quoted one of the canons that is often cited in suport of the "no prostrations on Sundays" rule. Here
it is with some additional notes, and here
is the other commonly-cited canon on the matter, from the first Council of Nicaea, again with notes.
I think that there is often a temptation to be too rigorous about our own interpretation of these things. A question to those of you who are adamant that prostrations are forbidden on Sundays: do you know, with absolute certainty, that the canons which forbid prayers "on bended knees" actually proscribe prostrations? The reason I ask is that it seems to me that the plain meaning of the text is that standing, rather than kneeling, is the position to be adopted for prayer on Sundays and the days of Pentecost, in honour of the Resurrection. There is no mention made of prostrating. This position of kneeling down for prayer, which is what these canons discuss, seems to me quite a different matter from making a prostration - a momentary gesture of awe and reverence.
When the Holy Chrism is brought out and when the pre-Sanctified Holy Things are removed from the tabernacle, a prostration is made, even if it is a Sunday. Similarly, as others have said, we prostrate at Sunday Matins on the feast of the Holy Cross if it falls on a Sunday, and also on the third Sunday of Great Lent. So I do not understand why such a prostration would be forbidden at the epiklesis. After all, these are not penitential gestures, such as kneeling, but rather are an act of worship and reverence before holy things.
The practice of the Old Ritualists also tells us that these prostrations on Sundays are not an innovation resulting from 18th-century western influence, but were the practice of the Russian church for centuries before the Nikonian reforms brought it in line with the Greek revisions over the centuries. Are we to believe that the pious faithful from this period of Russian church history, many of whom became great Saints, disregarded the canons and did not understand them, and that all of a sudden we, who are much wiser than they, have some great insight to which they were blinded? Or might it just be possible that they understood that kneeling down to pray and making a prostration are not the same thing?
In my early days of Orthodoxy, I picked up from rigorist converts that prostrations are absolutely forbidden on Sundays, and that is the practice I followed until recently, when I was confronted by all of the clergy making a full prostration at the epiklesis at an Hierarchical Liturgy on a Sunday. I was delighted to see this because making a prostration at this point is what my heart calls me to do. It seems the most natural thing in the world, and I found the rule incredibly restrictive. I asked my own bishop about this and his response was that there have long been two strains of thought on this matter, and that, while ROCOR practice generally
follows that of Jordanville (which, for all of the love that we have for it, we must not forget is only one monastery) in not making these prostrations on Sundays, they are
made in large parts of Russia, including Christ the Saviour in Moscow. He said that there is a place for such variety in the Church.
This is my own viewpoint, as well. If people are reticent about prostrating on Sundays and, out of honour of the Resurrection of our Lord, choose instead to make a reverence, I have no problem with this. The problem I have is when those of us who do wish to make the prostrations are accused of being uncanonical, disobedient, ignorant, and so forth, simply for paying honour and worship to the Saviour. There is something about the mindset behind this that does not sit easily with me.