Let me post a tangential, theoretical answer to supplement at least two other answers, already posted, with which I agree. You can make of it what you will.
Very occasionally, as might even be preferable to because, even in technical writing. The reason is as subtle as it is obscure. In a philosophical context, the Anglo-Latin stem cause can carry Aristotlean freight, implying a question as to whether the cause is material, efficient, formal or final. The Saxon conjunction as carries no such freight. The as is vaguer, of course; but English as English has its own, rather effective ways to consolidate what the French and the Greek regard as typically Saxon vagueness. The as might be all right in context.
However, my answer is merely theoretical. So far as I recall, I have never once written a sentence that simultaneously disqualified because on Aristotlean grounds and since by (as @Wayne has observed) confusion of temporal sequence (though I have several times written sentences that disqualified the one or the other); and, if I ever did write such a sentence, I probably would rewrite the whole sentence to avoid falling through to as as the third alternative. The as as a synonym for because is inadvisable because -- well, because it is inadvisable. It suggests poor education, somehow, and has long done so. I do not remember either Gibbon's or Burke's ever using as for because, for instance. If Twain put as in the mouth of a character of his, why did he do that? It never was to compliment the character's education, I don't think. That's English for you.
By the way, I very much like @Cerberus' sample sentence. It wants neither because nor since, precisely on Aristotlean and temporal grounds, whereas as works nicely there. However, that sample sentence is a rather rare case.