Put simply, the idiom is "all of a sudden," not "all of the sudden." That may be all you need from me on this matter, so if it is, feel free to click on out of here.
Most of you probably don't make this error, but I know you have seen it and heard it. What surprises me is not only how often I encounter this butchered idiom, but where I encounter it. I have read it in papers by graduate students in English, and I have heard it from the mouths of pretentious and pedantic newscasters and talking-head pundits on television.
It is difficult for young people to learn the proper forms when so much of the language they hear comes from the mass media, and the mass media so regularly offer up the wrong forms.
Even those young people who read are likely to do much of their reading in mass circulation newspapers and magazines. Unfortunately, those who write for such publications are often not well-versed in matters of grammar and usage, and even those who edit their writings--if indeed much editing is done at all, which I am beginning to doubt--may not be quite as knowledgeable in those areas as we might wish.
"All of a sudden" is an idiom. There is no logical or grammatical reason why we say "all of a sudden" rather than "all of the sudden." It's just that, until recently at least, no native speaker of English would say "all of the sudden," just as no native speaker of English would say "She was hit with a car."
True, idioms are shaped by widespread usage, so that if enough people over a long enough period of time say "all of the sudden," eventually that will become the preferred idiom, and someone many years hence will write an article deploring the fact that some benighted speakers and writers don't know any better than to say "all of a sudden."
But that day has not yet arrived, and until it does, the proper phrasing remains "all of a sudden," and those who use "all of the sudden" will be marking themselves as imperfectly educated, or at the very least as careless in their use of language.