Vision-based Continuous Sign Language Recognition (CSLR) aims to recognize unsegmented signs from image streams. Overfitting is one of the most critical problems in CSLR training, and previous works show that the iterative training scheme can partially solve this problem while also costing more training time. In this study, we revisit the iterative training scheme in recent CSLR works and realize that sufficient training of the feature extractor is critical to solving the overfitting problem. Therefore, we propose a Visual Alignment Constraint (VAC) to enhance the feature extractor with alignment supervision. Specifically, the proposed VAC comprises two auxiliary losses: one focuses on visual features only, and the other enforces prediction alignment between the feature extractor and the alignment module. Moreover, we propose two metrics to reflect overfitting by measuring the prediction inconsistency between the feature extractor and the alignment module. Experimental results on two challenging CSLR datasets show that the proposed VAC makes CSLR networks end-to-end trainable and achieves competitive performance.