Hot topic in the Catholic Forums:
"Attn. Christians of Various Traditions: Women & Head Covering ? - Catholic Answers Forums"
The question presented was: "What Christian Tradition do you belong to & at what time in it's history did it No longer be expected for Christian women of your Tradition to cover their heads full-time & when it's history did it no longer be expected for women at Church & during prayer And further, what reason was given for it to be acceptable for a Christian woman of your Tradition to be uncovered."
As always, there is some discussion of the first several centuries of Christian writings, also called the Church Fathers, and the phrase from the Apostle Paul: "... because of the angels."
No one can pinpoint for sure why the tradition of head covering in the churches faded away, but as the questioner proposes, it does seem to point to the era around the last century and the "women's lib movement". Others seem to not care when it did pass away, but are content that it did. Some interesting thoughts in places, if you care to peruse the pages of forum postings.