Spiking neural networks (SNNs) promise energy efficiency and offer a more brain-like alternative to artificial neural networks. However, training them on challenging tasks requiring credit assignment across long time horizons remains a significant challenge due to their discrete spiking interactions, which make the error landscape non-differentiable. A recent approach replaces the spike interactions with a surrogate gradient in the backward pass of gradient descent.\footnote{Neftci et al., \textit{Surrogate Gradient Learning in Spiking Neural Networks}, IEEE Signal Processing Magazine, 2019}\footnote{Rossbroich et al., \textit{Fluctuation-driven regime enables biologically plausible training in deep spiking neural networks}, arXiv:2203.06287, 2022} Yet, training SNNs with surrogate gradients is still prone to exploding and vanishing gradients, especially for temporally complex tasks. In this work, we tackle the challenge of temporal credit assignment in spiking networks using concepts from dynamical systems theory. We establish a link between the error gradient and Lyapunov exponents of the network dynamics to mitigate exploding and vanishing gradients in spiking network training. We introduce \textit{surrogate Lyapunov exponents}, computed with the surrogate spike function, which quantify the exponential temporal growth rate of small activity perturbations and predict error gradients in SNNs for tasks that require bridging long time horizons. We leverage differentiable linear algebra to regularize these surrogate Lyapunov exponents in a method we call \textit{surrogate gradient flossing}. This creates slow tangent modes that facilitate gradient signal propagation over timescales exceeding the intrinsic timescales of individual neurons. We demonstrate that surrogate gradient flossing improves training speed and success rate on tasks with long time horizons. Our approach uses dynamical systems theory to better understand and mitigate exploding and vanishing gradients in spiking neural networks. These insights and methods open avenues for improved training protocols for more brain-like models in theoretical neuroscience and neuromorphic computing, suggesting collective mechanisms for neuronal temporal credit assignment.