First, you are not alone. As you can see from the responses to your original post, there are many aikidoka across the world that care and are willing to provide support and advice for improvement, or to answer or discuss some of the many questions that overwhelm and baffle us as aikido students, and some of these helpful aikidoka happen to be female, like you and like me.
I don't often contribute to discussions, as I am also just a student. However, this particular question seems very pertinent to my own experiences and aikido journey, and since I was able to work through it and I don't see many similar experiences currently being shared, I feel obligated to "speak." I apologize in advance for the length and will try to at least organize the post.
After reading your question and everyone's posts, I see a situation similar to my own a few years ago and several good suggestions for improvement. I'll start with the suggestions I liked best, and then share with you what I did to reverse the roles and become a regular demonstration uke for Sensei.
Several posters recommended speaking to Sensei about your concerns in one way or another. If you are comfortable addressing the topic directly with Sensei, I like the approach someone mentioned of telling him you want to work on your ukemi, and asking what he'd recommend. Along these lines, I also like Lorien's idea of
asking Sensei to throw you around for a few minutes after each class.
As she explains in her post, benefits would include practice and guidance for you, and familiarity for him throwing you. Five minutes of ukemi with Sensei would also provide some serious opportunities for increasing ukemi endurance.
From your description, I agree with Mark in that I don't see it as "overt gender-bias," and can't speak to any particular reason you, as an individual, would be called as uke less often than your classmates. Regardless, just like in aikido itself, it's perhaps easier to focus on changing oneself and affecting one's own movement, and then see what happens to others around, than it is to try to change someone else.
PERSONAL UKEMI STORY
Personally, when I noticed I wasn't being selected as uke for practice, I saw it as an individual issue for me. I decided there must be something about ukemi I'm personally missing or could change. I chose a nonverbal remedy option to begin my ukemi improvement plan. I began to watch Sensei's favorite ukes, especially the people called repeatedly by both local and visiting instructors. I practiced with them whenever I could, and tried to see what it is that they did as uke. What was their connection and energy like? How did they move and react? And as I improved, I began to be called more as uke for demonstrations during practice first and then later at seminars.
Before practice, I would loosen up and make sure I was "round" and relaxed, and practice rolling. During practice, I tried to be aware of my ukemi as uke. This included trying to stay as connected as possible for as long as possible and trying to provide that "right amount" of initial and continued energy flow from your center to your partner's center. After a few months, and some ukemi adjustments here and there, Sensei apparently noticed some kind of improvement and I began to be included regularly in the rotation of Sensei's ukes during practice.
At one point in my practice, I was particularly frustrated with my technique and lack of aikido knowledge, ability, and improvement overall. I then decided that rather than try to improve everything at once, I needed to focus on one smaller goal, and of the two general choices of improving as uke or as nage, ukemi is something I was ready to learn, while good technique continued to elude me. I started asking senior students for extra advice and suggestions (such as aikiweb), especially whenever I found ukemi from a particular technique awkward. [If ukemi was awkward, maybe I was doing something wrong. How is a more natural way or safer way to fall? Sensei's uke didn't seem fazed at all; what did he do instead? ]
Two pieces of advice from sempai were (1) "practice ukemi to improve ukemi" because practice makes…well… better, and (2) to improve endurance, add extra conditioning, such as running. So, I started asking Sensei or a senior student for extra ukemi after class, and began running outside of class to increase my endurance for ukemi. When I began, one minute with Sensei was all I could handle before my legs refused to support me properly. This gradually increased to about five minutes, going all out. Longer than five minutes would require me to pace myself. Over the next one to two years, I also became a fairly regular seminar uke, for one particular instructor. I believe it helped to be able to get several reps shown in a short amount of time.
[Note, however, ukemi can also be expected to be very very slow, depending on your partner's familiarity with technique and what he or she is focusing on, whether you are injured and practicing on your own, or if Sensei is showing something and talking at length about the different steps as you go along. For a somewhat humorous example: "Uke should be really uncomfortable about here. You should have one hand here and one hand here. Keep your elbows down. Bend your knees. Notice uke's back foot, how she's on her toes and her foot is coming off the ground; that's a good sign. Not here, but here. Watch how uke hops… Now all you have to do is pivot/shift weight/let go and uke falls (…greatfully)."]
I am by no means an expert, and have so very much to improve. However, if anything from my journey thus far helps you in yours, you are welcome to it. I am very thankful to some of the folks from aikiweb who have donated their time to help me, especially with ukemi advice both online and in person. I hope you find the community you are looking for as well.