In open-domain question answering, a model receives a text question as input and searches for the correct answer using a large evidence corpus. The retrieval step is especially difficult as typical evidence corpora have \textit{millions} of documents, each of which may or may not have the correct answer to the question. Very recently, dense models have replaced sparse methods as the de facto retrieval method. Rather than focusing on lexical overlap to determine similarity, dense methods build an encoding function that captures semantic similarity by learning from a small collection of question-answer or question-context pairs. In this paper, we investigate dense retrieval models in the context of open-domain question answering across different input distributions. To do this, first we introduce an entity-rich question answering dataset constructed from Wikidata facts and demonstrate dense models are unable to generalize to unseen input question distributions. Second, we perform analyses aimed at better understanding the source of the problem and propose new training techniques to improve out-of-domain performance on a wide variety of datasets. We encourage the field to further investigate the creation of a single, universal dense retrieval model that generalizes well across all input distributions.