Anglican clergy have been invited to join the Roman Catholic church
A Church of England committee has backed away from a concession which would give traditionalists their own male bishops with independent powers.
The General Synod revision committee made the recommendations last month.
It suggested that these bishops might have full legal authority to operate independently of the diocesan bishop - who might in future be a woman.
But the committee now says it has failed to agree on what the independent powers should be.
Some Anglican clergy opposed to women bishops are considering an offer to join the Roman Catholic church.
Anglicans who convert could keep some of their traditions, the Vatican has said. They would join a special section that would let them keep aspects of Church of England liturgy.
The revision committee's abandonment of its proposed concession means that male bishops overseeing traditionalists would, in some cases, only be able to operate at the behest of women bishops.
BBC religious affairs correspondent Robert Pigott said that as things stand, the development seems likely to encourage more traditionalists to convert to Roman Catholicism.