Is it normal to reject a paper based on the review of a single referee?
It is normal. Often there is one referee who writes an extensive review, whose judgment weight heaviest with the editor. If there are 4 reviews, 3 are in the "publish" half of the spectrum but are brief (not adequately justifying the recommendation), and there is 1 "reject" review which extensively argues against publication, an editor will either have to apply his/her own knowledge of the field and decide which argument carries the day, or will need to request an additional review. Good editors do not just count up the plus and minus values, they have to evaluate the evidence in the reviews.

If you make the case for reconsideration, I think it should focus on the question of whether positive evidence in the reviews has been undervalued. There's not much you can do if the negative reviewer is (unbeknownst to you) The Leading Authority.