Single shot echo-planar imaging, traditionally used for dynamic susceptibility contrast (DSC) perfusion-weighted MRI (PWI), is not efficient for high resolution imaging due to T2* signal decay and poor compatibility with advanced reconstruction techniques. Spiral acquisition samples k-space more efficiently and is amenable to advanced reconstructions necessary for imaging at higher resolution and for multi-echo imaging. However, for high accelerations, spirals lack necessary k-space center training data. We enable low-rank-based reconstruction for multi-echo spiral acquisition by introducing progressive learning of temporal models. Our approach is demonstrated for multi-echo spiral DSC PWI with high spatial/temporal resolution (1.1x1.1mm/1.1s).