They are dying, and not very slowly. We have often posted on this topic. The reason is obvious: these churches have been co-opted, captured by soft or firm Lefties who have replaced the search for Truth for political attitudes. People want God, but they are delivering pet funerals.
I suppose you could call that one aspect of "the long march through the institutions." Non-profits and other sorts of do-gooder organizations are vulnerable to being corrupted by that sort of activism because they often attract a certain sort of person.
My Protestant church is bursting at the seams with tons of young couples and tons of little kids. I know our pastors pretty well, but have no idea what they think about any political or otherwise controversial topic. Nor do I care, because they view their job as one of saving souls through Christ and that's what they do. Lots of people hunger for that.
There are many reasons people take two hours on Sunday morning to go to church, but politics and trendy silliness are not among them.
From Douthat's Can Liberal Christianity Be Saved?
Today... the leaders of the Episcopal Church and similar bodies often don’t seem to be offering anything you can’t already get from a purely secular liberalism. Which suggests that perhaps they should pause, amid their frantic renovations, and consider not just what they would change about historic Christianity, but what they would defend and offer uncompromisingly to the world.
Absent such a reconsideration, their fate is nearly certain: they will change, and change, and die.
From Akasie: What Ails the Episcopalians - Its numbers and coffers shrinking, the church votes for pet funerals but offers little to the traditional faithful:
General Convention is also notable for its sheer ostentation and carnival atmosphere. For seven straight nights, lavish cocktail parties spilled into pricey steakhouses, where bishops could use their diocesan funds to order bottles of the finest wines.
During the day, legislators in the lower chamber, the House of Deputies, and the upper chamber, the House of Bishops, discussed such weighty topics as whether to develop funeral rites for dogs and cats, and whether to ratify resolutions condemning genetically modified foods. Both were approved by a vote, along with a resolution to "dismantle the effects of the doctrine of discovery," in effect an apology to Native Americans for exposing them to Christianity.
Re the latter, so much for mission work, I guess. "Gee, I'm sorry we told you about Jesus"! My view of ministry is simple. Preach the Word to all, visit the sick, inspire the marrying and comfort the bereaved. Mostly, preach the Word of God. What people decide to do with the lessons should be no concern of churches.