Local stake and ward prayer circles were organized and conducted until May 3, 1978, when the First Presidency announced that all prayer circles should be discontinued except those performed in a temple as part of an Endowment ceremony (See Spencer W. Kimball, N. Eldon Tanner, and Marion G. Romney, Letter to All Stake Presidents and Bishops. May 3, 1978; “Update,” 3 Sunstone 6, July-August 1978).

The reason for this change is unknown, but could have resulted, in part, from the explosive growth of the Church and the fact that prayer circles were usually organized by a member of the First Presidency or the Quorum of the Twelve Apostles (D. Michael Quinn, Latter-day Saint Prayer Circles. page 105).

Prayer circle wiki[1]

[Update 11/15/2016: I am wrong. This Book of Enoch was written by a 1970’s spin off version of the church after a missionary wanted to return to polygamy. Parley P. Pratt’s book of Enoch doesn’t mention True order of Prayer or veiled faces. But he did have one. I confused the versions of the Book of Enoch]

[Original content:] Book of Enoch that Parley P. Pratt had with him in 1844 mentions, “True order of Prayer.” and women having their faces veiled[2][/Original content].

How to construct your own altar for the prayer circle in your home[3], including a letter from the First Presidency in Brigham Young’s time.