Well, this left me a bit gobsmacked and from then on I made sure that all my emails to her began with a salutation (for almost all email I now use the greeting "Hi") and her name.
I also made sure that I sat down and considered this for a moment, worked out the problem and saw the resolutions to be made. Both for dealing with her, and for any other girls in the future. It turned out that over the previous two dozen emails or so that we had sent each other, I got into the habit of just replying without a greeting, without a salutation - in fact I was using email almost the same as text messages. When an email came in from her, I just replied to the salient point directly, maybe with a joke, maybe with an observation but with no "hi there" at the start -- just straight into a sentence. I do this with a few people and no one had ever called me on it, but here was a girl that was clearly unhappy.
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