Universal lesion detection has great value for clinical practice as it aims to detect various types of lesions in multiple organs on medical images. Deep learning methods have shown promising results, but demanding large volumes of annotated data for training. However, annotating medical images is costly and requires specialized knowledge. The diverse forms and contrasts of objects in medical images make fully annotation even more challenging, resulting in incomplete annotations. Directly training ULD detectors on such datasets can yield suboptimal results. Pseudo-label-based methods examine the training data and mine unlabelled objects for retraining, which have shown to be effective to tackle this issue. Presently, top-performing methods rely on a dynamic label-mining mechanism, operating at the mini-batch level. However, the model's performance varies at different iterations, leading to inconsistencies in the quality of the mined labels and limits their performance enhancement. Inspired by the observation that deep models learn concepts with increasing complexity, we introduce an innovative exploratory training to assess the reliability of mined lesions over time. Specifically, we introduce a teacher-student detection model as basis, where the teacher's predictions are combined with incomplete annotations to train the student. Additionally, we design a prediction bank to record high-confidence predictions. Each sample is trained several times, allowing us to get a sequence of records for each sample. If a prediction consistently appears in the record sequence, it is likely to be a true object, otherwise it may just a noise. This serves as a crucial criterion for selecting reliable mined lesions for retraining. Our experimental results substantiate that the proposed framework surpasses state-of-the-art methods on two medical image datasets, demonstrating its superior performance.