When is it time to cut loose from toxic family members?

Hello everyone,
I have never had a great relationship with my sisters. Oldest one is over a decade older than me, and is my half-sister from my parents previous relationship. There's been a lot of jealousy and sibling rivalry. I can appreciate there's two sides to an argument, but she's said some pretty bad things to me the worst one being that my mum forgot to take the morning after pill when I was conceived. This month I invited her and my other sibling to a prestigious event where I was meant to receive an award. I didn't mind so much if they couldn't make it or not, but I put the olive branch out there. But I've been ignored over the last couple of weeks. I still continue to do the sister/aunt thing of sending cards and gifts to families when there's a birthday and during the christmas period, but I am so depressed about things that I am just thinking of severing connections. My elderly mum is terminally ill, and has offered to have words with them about their behaviour. When is it the right time to cut your losses totally. I have younger family members that I continue to send cards/presents to but I feel like I have been ghosted. Any advice would be good.