Btukfyl

The original idea was a race of matriarchal desert nomads, but most desert nomad societies I could find as inspiration were strongly patriarchal.

I can change this aspect if I don't find a way to make it plausible, but I'd rather not since it's already incorporated in the worldbuilding. It doesn't need to be absolute -- I just need a plausible explanation for at least 70% of this species' societies being matriarchal.

I would also appreciate some environmental factors which would favor matriarchy.

Biological lifelong pair bonding (monogamy). This is rare, but does happen.

At least one reason males seek dominance in a society is to increase their access to mates, and thus have more children then other males, thus their genes are increased in the next generation.

Due to sexual differences between genders, only males tend to do this; specifically in humans a female can only give birth to perhaps twenty children in a "sexual career", but a male can father thousands of children in his sexual career. Therefore, there is an evolutionary upside for males to mate with as many women as possible, but there is no evolutionary advantage for women to do so.

Due to this dimorphism leading to competing mating strategies for spreading one's genes, men (and males in most wild animals) exhibit aggression and dominance over other males, to prevent them from mating and secure more mates for the "alpha". By the same token, in humans with a culture, it serves men to dominate both men and women to ensure their own ready access to reproductive opportunity.

This is true whether the result is the actual production of many children or not; the instinct to take control and subjugate others (by brute force or intelligent strategy) is still there, and stronger in males than in females.

An antidote for that, as a trait, would be lifetime pair bonding, eliminating the need for men to compete for women. Excerpts from the link:

The few animals that do stick together are providing scientists with valuable clues about the biological basis of fidelity. One of the most studied animals in this regard is the mouse-like prairie vole. A male vole will prefer to mate exclusively with the first female he loses his virginity to. And his faithfulness approaches a kind of fanaticism: Far from trying to woo other females, a mated male vole will actually attack them.

In recent years, scientists have traced these unusual behaviors to levels of certain neurotransmitters in the rodents' brains. Interestingly, one of these, dopamine, is also implicated in drug addiction in humans.

That's a plausible explanation for your species too: The female chooses a virgin male, and (biochemically speaking) the male becomes love-addicted to the female for life, he doesn't want to mate with any other female, and the only way for him to get his sex-fix is to please her, which he wants to do. He's literally not capable of being attracted to or aroused by another female.

In a way, you extend the "fallen into crazy love" phase of the relationship indefinitely, for the male. As part of pleasing her (and not suffering from the withdrawal symptoms of being denied sex with her) he lets the woman be in charge and make the decisions.

Presto, Matriarchy.

Postulating a cognitive aspect to sexual dimorphism, where the females are the brains of the clan/tribe/species. Couple this with males being subject to musth, like elephants - where their sex hormonal drives are so strong they cannot be entrusted to leadership. Highly intelligent matriarchal societies would have more subtle ways of co-opting the males into cooperation, including withholding sex, ritual restraints, cultural taboos.

Postulating a reproductive bias toward females which tends to keep males in the minority within populations.

Postulating the female controls paternity, as a means of modulating male behavior, enhancing female control at the most basic level.

Postulating females as the larger of the sexes (as in hyenas). Less plausible.