I don't know how anyone else holds onto faith; I just know how it works and how I want it to work for me.
Some who "lose their faith" remain in the Church; others leave. Some reconcile the dissonance and find a measure of peace; others don't and remain miserable. For the first group, the peace and community and family are more important than complete confidence and total lack of doubt, so they "put their issues on a shelf" and walk away from them for a time; for the second group, perfect understanding now takes first priority and overshadows everything else. Frankly, I think that points more to how each of us defines "faith" than it does about how we define "truth".
If by "faith" we mean "certainty about our religious beliefs", I agree that losing it might not be a conscious choice - that events and exposure to difficult concepts can rob people of certainty. That seems to be what many do - defining "faith" as "testimony" or "certainty" or "lack of doubt". If, however, we mean the "substance of things hoped for", I think many who are no longer active participants in The Church have not lost that hope and, therefore, have not lost their faith. In the face of what they have described, I think that's spiritual "evidence of things not seen" producing a conscious choice to not give up - to "endure to the end" in faith, without certainty.
I think the "problem" is that too many of us teach the universal possibility of personal certainty - in direct contradiction of our own scriptures that extol "simple faith" and assert that not all can "know". Without those unrealistic expectations, I believe much of the "dissonance" would disappear, since it would be ok simply to exercise faith and maintain hope in the face of uncertainty.
I also think that there are some people who simply lack "the faith gene" - who simply must understand something perfectly before they can accept it. I would argue that these people never possessed "faith" in the first place, so they can't lose it. Finally, I don't believe someone can "choose" to lose something they didn't "choose" to obtain or find. The challenge for such people to is accept the need for faith and quit demanding certainty.