A couple of things from your post stood out to me. Is this just about your brother not responding or is this about how much his and his family's lack of response to you hurts?
As others have said Men more often than not think it's the women's job to keep contact/correspondence going and therefore they can be neglectful. That's sad, it's wrong, it hurts but can be how they are. Is your brother and his family in this mould? If so make your choice about how you go forward in ways that don't leave you feeling hurt and ignored. Then address the question of your promise.
At your Mum's request, you promised to keep in touch with your brother. You have done your best to keep that promise.
So here's my first question - Are you trying to figure out if you can Let Go of Your Promise ?
If that is the emotional concern you are struggling with may be your way forward is to ask yourself some questions.
Such as, would your Mum have asked you to keep your promise even when contact came From you To your brother was NOT returned and therefore caused you hurt?
I'm not sure many people would ask a loved one to keep a promise if doing so would continually hurt the loved one. Would your Mum have asked you to keep being hurt? I wouldn't have thought so but she was your Mum and you knew her. (I don't think she would have knowingly put you in a painful situation)
The questions are :- Are you keeping the contact going Only because of your promise?
Or YOU Need to have contact with your brother ?
If you are Only keeping the promise you made I think you can find ways to give Yourself Permission to let go of the promise and stop the pain his lack of response causes you. See above.
If, however, this is about Your Need for His approval/recognition of your being one of his loved ones is what is the real cause of your distress, that's a lot harder to deal with.
If this you trying to Take Care of that part of you that wants to still BELONG, to still have a connection to your Childhood Family and he and his family are not engaging with you that may be where your hurt is coming from.
If your keeping contact is more about a need for Family and Belonging then I would suggest you find some counselling/therapy. That situation is painful and not easily managed alone, get help and support to work through IF that is the bigger issue you are dealing with.
He is from what you say all that you have left of your Childhood family and you have had a number of losses. Have you had any Bereavement Counselling?
If your hurt is coming more from that feeling of loss and not being part of a family have a look at Adult Orphan and other resources on the net.
I had an awful few moths of dealing with being an Adult Orphan when my adopted Mum died even though I had a younger sister and adopted brothers, a husband and 2 daughters. Fortunately I had some good people around and I already knew about the Adult Orphan concept.
I hope you find a way though your situation. While you are dealing with whatever the cause please take extra care of yourself. Be as gentle with yourself as would your child if they were dealing with this. Best os Luck