Is the sister sinful if she refuses to sit alone with her brother, and he consequently severs ties with her, and does she bear the responsibility for breaking kinship ties?

If there is a fear of fitna (strife/temptation) from one of a woman's mahram (unmarriageable kin), or if suspicion arises concerning him, then he must be treated as a ghair mahram (non-mahram); this is to block the means (to sin) and ward off fitna. Thus, a woman's refusal to be in khalwa (private seclusion) with her brother is obligatory if there is suspicion or fitna, and this is not considered a severing of kinship ties, as visits and maintaining ties can occur without khalwa. If this refusal leads to a severing of kinship ties on the brother's part, then the sin is upon him, and she will be rewarded for it. If the brother's harm cannot be repelled except by shunning him, then there is no harm in that, for a graceful shunning is better than harmful association.