This paper presents a study on the automatic detection of mental health issues among young people through social media posts in Vietnamese, a low-resource language. To this end, we introduce a manually annotated corpus with two labels (i.e. positive and negative) indicating whether a post exhibits signs of negative mental health or not. The data set faces a class imbalance problem, where the majority of posts belong to the positive class. To address this, we propose a model architecture based on recent advancements in transformer (i.e. pre-trained BERT model) technology. This architecture has two main key features. First, instead of relying solely on conventional cross-entropy loss, our model combines it with DSC loss, a function commonly used in image segmentation to address imbalanced learning. This weighted combination harnesses the advantages of both losses: cross-entropy loss aids in making accurate overall predictions, while DSC loss improves the model’s ability to handle the class imbalance. Secondly, to overcome the token limit imposed by transformers, we summarize the posts before inputting them into the model. Experimental results in our newly constructed dataset demonstrate the effectiveness of this approach. Summarization significantly improves overall performance, and the combined loss method increases the F1 score by 1.89% compared to the cross-entropy loss alone and by 1.04% compared to the DSC loss alone.