Is this a sexless relationship

I have been in a lesbian relationship for a few years. I'm beginning to think my partner is Asexual. She does not like to be touched in anyway at all. She really doesn't like anything sexual. Not even dancing due to close
Contact. I have tried everything I can think of to change her mind. So don't suggest dressing up sexy or massages or cooking a nice dinner etc..
To try to make me happy she fingers me for a few minutes maybe once a month. And it's like a chore for her. We hardly date also. I feel lonely and she seems distant at most. I have discussed this with her a few times and even suggested separating but she gets horribly upset at the idea of us apart.
I am attractive. She is younger by a decade ( it's nothing related to age or
a medical issue). My past relationship the sex was amazing and for hours but I don't expect her to perform the way my ex did. And I am not comparing. It is hard tho going from awesome to nothing. So you can see my frustrations.
My question is, would one consider being fingered a few minutes once a
Month still a sexless relationship. Their is no passion or intamacy. She does like
to cuddle but always too tired from work. ( I don't like cuddling because I am so frustrated with feeling lonely that I begin to think that maybe a cuddle
Will lead to more and it never does, I then secretly get more upset).
I suppose if being fingered once a moth for a few minutes is considered sex then I'll deal with it an accept it for what it is.