My theory, and I don't think it can be proven or disproven with the data that we have, is that Unitarian Universalism was revitalized in the 1990's and 2000's by the influx of gays, lesbians, bisexuals, transgender people, and queers. Not just numerically, but also culturally and theologically. And this influx followed closely after the dramatic rise in the number of female ministers.
Neither of these events were unique to Unitarian Universalism, especially the increase in female ministers, but both proceeded with less opposition in our denomination than others.
Unitarian Universalism has had an influx of converts, many of them younger that our mean age, many with children, many with frustrated aspirations for ministry. It is hard to imagine that Unitarian Universalism would be still around without them.
I think that this history offers much insight into our mission, our core purpose and DNA.
The fiery core that gives liberal religion its energy is the process of self-possession: a person laying claim to their own self. It can be self-identity: "This is who I really am!", a "coming out process". It can be self-invention: "This is who I intend to be from now on." It can be self-commitment: "These are the causes or the people for which I offer my loyalty and effort." It can be self-consecration: "This is the spiritual path I have chosen" or "These are the promises I make."
Self-possession is the result of acts of will, which are the creation of energy, which demands to be expressed.
In short, battery pack of liberal religion is people exercising their will to become the subject of their own lives, rather than the object of others. When we are no longer in touch with that process of individual self-possession then we wither.
It is our mission to bring about that transformation in people. Our churches and congregations are places where people can perform that transformation, where they can display the selves they intend to be, where they can get some witnesses to their changes.
Our small success in resisting the decline of mainline in the past decades has come from the fact that we living out our mission of empowering self-possession in a very concrete and effective way, with people who have needed it.