We could look at through a different lens and state that if you aren't jumping into startup after startup - successful or not - are you even an entrepreneur?
Well, that's sort of my point... serial entrepreneurs are the norm. Perhaps we should come up with a term for those rare entrepreneurs who are satisfied with a single attempt at the business game...
I would just say it's something entrepreneurial they are doing, doesn't per say make them an entrepreneur - perhaps it does though; If you're learning a musical instrument, are you not a musician? Maybe not a professional. Professional Entrepreneur vs. Amateur? :P Serial Entrepreneur has a better ring to it, though it really is just someone who is an entrepreneur IMHO.