A lot have been said about what is a professional photographer. We seem to forget there a lot type of client. The one here we are discussing are the type of client do not care what ever you are professional or not. They hire some one to do a job cheap, if he screw up he to blame and not to hire again. If they have the chance again they will exploit other (may they be hobbyist, new budding photographer, part time freelancer who have nothing better to do or even professional photographer). To them it is good business practices, buy low sell high.
But can we fully put the blame on them fully? The answer is "NO". They made a offer, if anyone of us(the photographer) take the offer. We have unwillingly allow such exploitation in our market.
So to answer the question what a professional photographer, I offer two:
In PPAS' (Professional Photographer Association Singapore) term, a professional photographer is a person who make his livelihood full time as photographer for more then two years, with a creditable portfolio of clients and more then 70% of his income come from photography services.
In my personal term a professional photographer is a person who can present himself professional to his client. By offering them creative solution to their photography needs and at same time make a decent living as a business person.