Civilisation (or civilization) is a sometimes controversial term which has been used in several related ways. Primarily, the term has been used to refer to human cultures which are complex in terms of technology, science, and division of labour. Such civilisations are generally urbanized.

It should not need to happen more than once - and there are no signs that it has done so.

This isn't a really helpful definition for our purposes. How complex does technology and division of labor need to be? There's division of labor in hunter-gatherer groups for example. I would agree that by almost all expansions of this definition neanderthals didn't make it, and that H. sapiens is the only species to have done so that we are aware of.

I am, however, puzzled by your statement that civilization arose only once. Do the New World civilizations of the Incans, Mayans, and Aztecs not count? I would think that the separation of the Old and New World would then necessitate at least two independent occasions where civilization has arisen.