No, I don’t. When I read a proof in Euclidean geometry, I have no “choice” whether or not to accept it. If the proof is sound, I must accept it; if the proof is flawed, I must reject it. There is no choice involved. It doesn’t depend on my will, taste, whim, desire, mood, etc.
If the jailer hears that he can be saved if he believes a man rose from the dead, he may well wish that such a thing were true, but he can’t make himself believe it merely on a wish. Not if he is a rational human being. He has to reason out whether or not a man could rise from the dead, and whether or not, even if such a thing were possible, that would provide a mechanism to erase his sins. And if he decides either of those questions in the negative, then he has no “choice” to believe he can saved in that way; reason would force him to reject that possibility, no matter how badly he wanted it to be true.
Yes, faith can be lost, but not by an arbitrary act of choice, as if someone can will to have faith on Monday, then will again to lose faith on Tuesday, then will again to have faith back on Wednesday. Faith is lost when people’s view of the world, God, the soul, sin, etc. change as they come to think differently about the world. Many fundamentalists have lost their faith in the Bible because years of study of evolution have altered the way they look at the age of the earth, the origin of man, etc. They didn’t just decide: “I was a fundamentalist yesterday, but I think I’ll be an atheist Darwinian today.” The change wasn’t from an act of will, but from a process which transformed their understanding of what was real and true. They now no longer thought about the world they way they did before, and it was the change in thought that caused them to lose faith.
You apparently have a picture of faith as “choosing to believe something, even it seems to go against reason and evidence, because one really wants it to be true.” But I would deny that this is what “faith”, properly understood, means.