Automatically generating issue-reproducing tests is essential for debugging and regression prevention. Recent advances show that large language models can effectively perform this task, but their reliance on extremely large parameter scales limits practical deployment. In this paper, we propose SLIT, an execution-grounded framework that enables small language models to generate effective issue-reproducing tests. SLIT formulates issue reproduction as an execution-guided exploration problem and optimizes policies with reinforcement learning over execution-based rewards. To improve inference-time exploration, SLIT further introduces diversity-augmented test construction and a learned scoring model to select effective reproducing tests. Experimental results on SWT-Bench-Verified indicate that the 14B-parameter model achieves a resolve rate of 46.2%, achieving competitive performance against prior approaches that rely on larger models. These results demonstrate the effectiveness of SLIT and highlight the viability of execution-grounded small language models for issue-reproducing test generation.