This study examines Sexual Homicide (SH) cases, analyzing the transition to cold cases through a non-discretionary lens. Utilizing the SH International Database, it explores the interplay between offender behavior, victim characteristics, and crime context. Advanced methodologies, including sequential logistic regression and Artificial Neural Networks, identify key predictors of case resolution. Results highlight the critical influence of victim intoxication, high-risk activities, and the location of the victim's body on case solvability. The study also reveals the significant role of offender forensic awareness and the complexity of crime scenes in hindering case resolution. These findings underline the multifaceted nature of SH cases, emphasizing the importance of understanding the nuanced interplay between victim, offender, and contextual factors in solving these challenging cases.