Artificial intelligence (AI) translation systems, which seek to address communication barriers among Deaf and Hard-of-Hearing (DHH) communities, often experience repeat cultural failure based on their incompetence to realize the rich cultural complexity and emotional depth embodied in the signed languages. A systematic study indicates recognizable patterns of cultural error, such as the threatening normalization of interpreted, non-native data and the failure to focus on the sensitive linguistic aspects, especially non-manual signs that bear grammatical and affective significance and meaning. In order to address these systemic failures, this paper suggests a Cultural Context and Error Framework of AI Translation (CCEF-AI) including an evaluation taxonomy, which recommends the mandatory addition of layers of cultural metadata, hybrid human-AI collaboration on high-stakes settings, and metrics that go beyond superficial measures of accuracy rating. Finally, equitable access would require a general effort towards inclusive, adaptive, community-informed AI design where Deaf leadership leads the agenda and development processes of research to ensure the erosion of linguistic rights and systemic bias are prevented by implementing research-based interventions and solutions.