Word for a person who loses or has lost faith?

if by losing faith you mean the person does not believe anymore, then the word that comes to mind is 'apostate' - someone who renounces/abandons his a religious or political belief or principle.

http://www.thefreedictionary.com/apostate

It depends to a fair degree on the context.

One who has lost faith might be disillusioned: freed from or deprived of illusion, belief, idealism, thus realizing that a belief or an ideal is false; or disenchanted (freed from illusion or false belief). Certainly one would expect an initial disappointment or discouragement by the loss of one's hope in someone or something that one discovers to be less good than one had believed.

I'm not religious. I was as a child, and like lots of people... [I] became very disillusioned with the whole thing. - Natascha McElhone

If not saddened, one can be disabused of a falsehood or misconception, or even enlightened (factually well-informed, tolerant of alternative opinions, and guided by rational thought.)

In less enlightened times, the best way to impress women was to own a hot car. But women wised up and realized it was better to buy their own hot cars so they wouldn't have to ride around with jerks.
- Scott Adams

There isn't a common word for it, so it rather depends on what spin you want to put on it. Recovered X is used by some former believers in the sceptic movement to describe themselves while former X is rather more neutral but doesn't necessarily have the connotation of lost faith you're looking for. Disillusioned X or disenchanted X carry a connotation of a particular manner of leaving the faith and perhaps lingering doubt. Lapsed tends to refer to people who continue to partake in the wider culture of a religion but don't regularly attend or have strong beliefs. Apostate could be used but it's a relatively uncommon term and carries quite a bit of baggage.

Christians might refer to themselves as having a "crisis of faith" during periods of doubt.

"Ex-believer" might be the most neutral word for it, without too much emotional baggage. And it does not apply exclusively to religion too, or spirituality.