Semiparametric language models (LMs) have shown promise in continuously learning from new text data by combining a parameterized neural LM with a growable non-parametric memory for memorizing new content. However, conventional semiparametric LMs will finally become prohibitive for computing and storing if they are applied to continual learning over streaming data, because the non-parametric memory grows linearly with the amount of data they learn from over time. To address the issue of scalability, we present a simple and intuitive approach called Selective Memorization (SeMem), which only memorizes difficult samples that the model is likely to struggle with. We demonstrate that SeMem improves the scalability of semiparametric LMs for continual learning over streaming data in two ways: (1) data-wise scalability: as the model becomes stronger through continual learning, it will encounter fewer difficult cases that need to be memorized, causing the growth of the non-parametric memory to slow down over time rather than growing at a linear rate with the size of training data; (2) model-wise scalability: SeMem allows a larger model to memorize fewer samples than its smaller counterpart because it is rarer for a larger model to encounter incomprehensible cases, resulting in a non-parametric memory that does not scale linearly with model size. We conduct extensive experiments in language modeling and downstream tasks to test SeMem's results, showing SeMem enables a semiparametric LM to be a scalable continual learner with little forgetting.