From my experience going NC with family is usually a result of a life time of hurts and family dysfunction. Communication is usually poor, wrongs are ignored, abuses are brushed under the carpet and the culprits rarely have self awareness or apologies for their victims. Not saying that's the case with your relationship but that's how it was with my family.
My brother was my mother's golden child, he was her sidekick in scapegoating me, never disciplined and grew up thinking it was okay to be rude, dismissive and at times downright callous towards me. Like a lot of scapegoats I turned myself inside out to please him, to try to get his attention and validation. It didn't work.
Crunch time came when I decided to get away from our toxic mother and out of my toxic marriage. It then became crystal clear where I stood with my brother. He threw me under the bus with the rest of the family and sided with my exH. I did try to talk to him about it but he turned it back on me, the usual scapegoating crap that I was the crazy one.
Roll on around twelve years in which I was completely ignored, his wife also cut me off on behalf of my mother, he turned up on the doorstep wanting to be friends. He has now seen the light and gone NC with our mother. Too late. Again no self awareness or remorse for the hurt and damage he caused me. Brushed over. The impression I got was that HE was seeking my support at being isolated from 'the family '.
To answer your question, if he had shown any insight in his behaviour towards me, any reflection on his abuse of me in childhood and previously, any remorse , we could work through this. I don't trust him and will never let him back in. I'm not saying I'm all innocent in this. Dysfunctional familys suck but it is possible to heal with good communication.
If I can give you some advice, I would get some therapy for yourself, look at anything you may have done, unconsciously, to cause hurt to your sister. This could be your sister's hang up, it may not, but she's hurting about something. Write her a truly heartfelt apologetic letter and ask for forgiveness. That would have worked with my brother. It's the stunning lack of self awareness that stings with me. 💐