Temporal Difference (TD) learning is ubiquitous in reinforcement learning, where it is often combined with off-policy sampling and function approximation. Unfortunately learning with this combination (known as the deadly triad), exhibits instability and unbounded error. To account for this, modern RL methods often implicitly (or sometimes explicitly) assume that regularization is sufficient to mitigate the problem in practice; indeed, the standard deadly triad examples from the literature can be ``fixed’’ via proper regularization. In this paper, we introduce a series of new counterexamples to show that the instability and unbounded error of TD methods is not solved by regularization. We demonstrate that, in the off-policy setting with linear function approximation, TD methods can fail to learn a non-trivial value function under any amount of regularization; we further show that regularization can induce divergence under common conditions; and we show that one of the most promising methods for mitigating this divergence (emphatic TD algorithms) may themselves diverge under regularization. We also demonstrate such divergence when using neural networks as function approximations. Thus, we argue that the role of regularization in TD methods needs to be reconsidered, given that it is insufficient to prevent divergence and may itself introduce instability. There needs to be much more care, both practically and theoretically, in the application of regularization to RL methods.