Unfortunately for me, it is by nature an unequal relationship. I have to take my cue from my sensei as to how the relationship goes. I feel like my only options are to accept my role as a student only or leave. What is hard about it for me is that it is a small dojo and I spend quite a bit of time there. To not be included in a social group within the dojo makes training there very lonely.
I always thought of Aikido as not just being the training and is more about the connections that are created through training. It just feels very hurtful to be excluded by the very person who taught me that.
Am I missing something? Should I not allow those connections to be broken? Or am I supposed to ignore how this behavior makes me feel and just shut up and train? Very confused.
My first advice would be to not think in terms of false dichotomies: it's either this, or it's that; I have choice A, or I have choice B. Focusing on what you perceive as your choices can blind you to other possibilities. And, in fact, I believe that one of your perceived choices is not available to you. You can't unilaterally create a relationship with someone if they don't want it, and that has nothing to do with who's the sensei and who's the student: every human being has autonomy, if they choose to exercise it, and can't be compelled to relate to you in the way that you want.
As for aikido being "more about the connections", that may be true for you, that you value the interpersonal relationships more than your training. Depending on how much more you value them, it could be a problem. I think that those who value their dojo primarily as a social outlet are bound to be disappointed eventually, and come to a place where their dojo fails them in that regard, simply because that's not the dojo's purpose, and it's not why others are there. I've seen a number of people go through this -- some were kind of isolated outside the dojo and may have been using it in an unhealthy way, others were as well-adjusted as anyone I know -- and eventually they all had to face the fact that they liked the dojo but didn't care so much about doing the aikido. If it's talking to your friends or going for beers afterwards that brings someone into the dojo, and not the training, it's probably not going to work out.