All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If a relative apostates [or commits an act that takes him out of the fold of Islam], then this does not prevent one from keeping ties with him. This is because it is confirmed that Asmaa' Bint Abi Bakr said: “My mother came to visit me while she was a polytheist at the time of the Prophet so I asked him [the Prophet]: “My mother came wishing that I will be kind to her as her daughter, shall I keep ties with her? He said: “Yes, be dutiful to your mother.” [Al-Bukhari and Muslim] For more details, see Fatwa 94482.
Therefore, you should keep ties with your sister provided you are not harmed in your religion and your worldly matters. However, you should endeavour to call her to return to Islam, and you should not despair from doing so.
Among the best means of Da’wah (calling people to Islam) is to seek the help of Allaah, be kind to the person one calls, and supplicate Allaah earnestly and not be in a hurry to get the result.
For more benefit, please refer to Fatwa 87672.
Allaah Knows best.