Stripe-like space target detection (SSTD) is crucial for space situational awareness. Traditional unsupervised methods often fail in low signal-to-noise ratio and variable stripe-like space targets scenarios, leading to weak generalization. Although fully supervised learning methods improve model generalization, they require extensive pixel-level labels for training. In the SSTD task, manually creating these labels is often inaccurate and labor-intensive. Semi-supervised learning (SSL) methods reduce the need for these labels and enhance model generalizability, but their performance is limited by pseudo-label quality. To address this, we introduce an innovative Collaborative Static-Dynamic Teacher (CSDT) SSL framework, which includes static and dynamic teacher models as well as a student model. This framework employs a customized adaptive pseudo-labeling (APL) strategy, transitioning from initial static teaching to adaptive collaborative teaching, guiding the student model's training. The exponential moving average (EMA) mechanism further enhances this process by feeding new stripe-like knowledge back to the dynamic teacher model through the student model, creating a positive feedback loop that continuously enhances the quality of pseudo-labels. Moreover, we present MSSA-Net, a novel SSTD network featuring a multi-scale dual-path convolution (MDPC) block and a feature map weighted attention (FMWA) block, designed to extract diverse stripe-like features within the CSDT SSL training framework. Extensive experiments verify the state-of-the-art performance of our framework on the AstroStripeSet and various ground-based and space-based real-world datasets.