In an article by Father Longenecker it is predicted that progressive Christianity will soon die out whereas historic Christianity will remain. Here are his definitions:
The historic Christians believe their religion is revealed by God in the person of his Son Jesus Christ, and that the Scriptures are the primary witness of that revelation. They believe the church is the embodiment of the risen Lord Jesus in the world and that his mission to seek and to save that which is lost is still valid and vital. Historic Christians believe in the supernatural life of the Church and expect God to be at work in the world and in their lives.
Progressive Christians believe their religion is a historical accident of circumstances and people, that Jesus Christ is, at best, a divinely inspired teacher, that the Scriptures are flawed human documents influenced by paganism and that the church is a body of spiritually minded people who wish to bring peace and justice to all and make the world a better place.
In the article he gives eleven reasons, all of which are important. Over all I think he’s right. Rodney Stark observed this empirically:
Not all denominations shared in the immense rise in membership rates, and to the degree that denominations rejected traditional doctrines and ceased to make serious demands on their followers, they ceased to prosper. The churching of America was accomplished by aggressive churches committed mitted to vivid otherworldliness.
Roger Finke;Rodney Stark. The Churching of America, 1776-2005: Winners and Losers in Our Religious Economy (Kindle Locations 78-80). Kindle Edition.
What is deemed progressive Christianity by Longenecker will, in my opinion cease to exist on a long enough timeline because people who practice religion merely as a matter of identity are typically less concerned about dogma and practice than those who convert. Progressive Christianity does not convert or tend to evangelize. Therefore, it will either morph beyond any resemblance to historic Christianity (which it is close to doing) or it will simply die out by attrition and low birthrates.
Give his article a read.