Detecting persons using a 2D LiDAR is a challenging task due to the low information content of 2D range data. To alleviate the problem caused by the sparsity of the LiDAR points, current state-of-the-art methods fuse multiple previous scans and perform detection using the combined scans. The downside of such a backward looking fusion is that all the scans need to be aligned explicitly, and the necessary alignment operation makes the whole pipeline more expensive -- often too expensive for real-world applications. In this paper, we propose a person detection network which uses an alternative strategy to combine scans obtained at different times. Our method, Distance Robust SPatial Attention and Auto-regressive Model (DR-SPAAM), follows a forward looking paradigm. It keeps the intermediate features from the backbone network as a template and recurrently updates the template when a new scan becomes available. The updated feature template is in turn used for detecting persons currently in the scene. On the DROW dataset, our method outperforms the existing state-of-the-art, while being approximately four times faster, running at 87.2 FPS on a laptop with a dedicated GPU and at 22.6 FPS on an NVIDIA Jetson AGX embedded GPU. We release our code in PyTorch and a ROS node including pre-trained models.