The development of safety cases has become common practice in many safety critical system domains. Safety cases are costly since they need a significant amount of time and efforts to be produced. More- over, safety critical systems are expected to operate for a long period of time and constantly subject to changes during both development and operational phases. Hence, safety cases are built as living documents that should always be maintained to justify the safety status of the associated system and evolve as these system evolve. However, safety cases document highly interdependent elements (e.g., safety goals, evidence, assumptions, etc.) and even seemingly minor changes may have a major impact on them, and thus dramatically increase their cost. In this paper, we identify and discuss some challenges in the maintenance of safety cases. We also present two techniques that utilise safety contracts to facilitate the maintenance of safety cases, we discuss the roles of these techniques in coping with some of the identified maintenance challenges, and we finally discuss potential limitations and suggest some solutions.