Another bit of reflection... where fantasy and science overlap.
Some anthropologists assert that sex (the male-female thing... not the fun thing) is a cultural construction. If you mentioned this to Prof Steve Jones (UCL), would he laugh in your face? I'm not entirely sure that he would. True enough, chromosomes and sex hormones dictate the bits you're born with and can affect chemicals in the brain (and therefore behaviour). But one of the things Steve Jones and many other biologists argue is that it is impossible (or incorrect) to try to disentangle nature from nurture in the construction of a person. He would say that our genetic make-up is key to our personalities, and that frequently, it is our environment that causes genes to be expressed in a certain way (i.e. if you have an obesity-linked gene, obesity will only be expressed if food is abundant enough).
So how does this link to The Fireblade Array? Well, Artemi is reborn again and again. She is essentially a clone of her previous self, or perhaps a series of identical twins spread across time. In each life she displays very similar personality traits, even falling in love with the same man.
What I have tweaked here is that she looks identical to her previous self each time, whereas anyone who has met/knows/is a set of identical twins will observe that they are never quite visually identical. These differences are a result of environment, the way environment can alter gene expression and a bit of chaos. Identical twins also tend to have personality differences, which vary in magnitude between sets. It has been observed that, when compared to a general population, the relative differences between twin reactions to various stimuli actually tend to be quite small. And you can always argue that this is due to their shared upbringing... which is why researchers often look to compare identical twins who've been separated. But, generally speaking, it is the case that identical twins appear very different when compared only to each other, and very similar when compared to the rest of the world.
These similaries (and differences) are thought to be influenced by differing proportions of genetics, environment and complex heritability. So, height may be mostly genetics, IQ might be 60% genetics and autism is affected by a variety of pathways and stimuli that are very difficult to extrapolate. And don't forget epigenetics, where the environment can alter the way your DNA is packaged and read.
Given that Artemi can only ever be guaranteed the same set of genetics each time she reappears, how is it that her differing environments produce a very similar woman? Well, she is brought up by the same father in books 1 and 2. She's also got thousands of years of memories bouncing around inside her head that she remains in denial about until she's twenty-three. Those would have to affect her personality in some way (but in relatively equal measure across her later lives).
There are, however, some differences in her behaviour between books one and two. In book two (before she has her memories) she is far more assertive, perhaps more aggressive and more outspoken than before. She is also much more aware of her own feelings.
As for her unchanging visual appearance, I perhaps took some liberties with the fantasy world for Morghiad's sake... or maybe after twenty years most people would fail to remember her well enough to notice the differences.
In terms of what she is able to do: some of it is set by her memories, but she clearly has developed her skills to a greater extent in certain areas than others (i.e. fighting). However, I think after enjoying as many lives as she has, she would have developed other interests. These may make appearances in later books ;-)
To come back to my opening sentences, I think the roles associated with sex are cultural constructions which may have their origins in sex-linked characteristics. However, there are always people who do not fit or conform (this is the rule rather than exception in literature, where tough women are nothing new) - but many aspects of their personality owe a great deal to their genes. Yet such roles are not the same things as skills...
I think that, in terms of skills, our brains are actually very plastic - and very capable of learning things outside of certain stereotypes. It's just the confidence, drive, and energy to do these things that can be altered by a combination of our genetics and societal expectations. I've only really explored this to a very limited degree in my books - but I wanted you to know that I'd thought about it :-D