Leveraging social media for stress detection has been growing attention in recent years. Most relevant studies so far concentrated on training a stress detection model on the entire data in a closed environment, and did not continuously incorporate new information into the already established models but instead regularly reconstruct a new model from scratch. In this study, we formulate a social media based continuous stress detection task with two particular questions to be addressed: (1) when to adapt a learned stress detection model? and (2) how to adapt a learned stress detection model? We design a protocol to quantify the conditions that trigger model's adaptation, and develop a layer-inheritance based knowledge distillation method to continually adapt the learned stress detection model to incoming data, while retaining the knowledge gained previously. The experimental results on a constructed dataset containing 69 users on Tencent Weibo validate the effectiveness of the proposed adaptive layer-inheritance based knowledge distillation method, achieving 86.32% and 91.56% of accuracy in 3-label and 2-label continuous stress detection. Implications and further possible improvements are also discussed at the end of the article.