Product search has been receiving significant attention with the development of e-commerce. Existing works recognize the importance of personalization and focus on personalized product search. While these works have confirmed that personalization can improve the performance of product search, they all ignore the few-shot learning problems caused by personalization. Under the few-shot setting, personalized methods may suffer from the data-hungry issue. In this paper, we explore the data-hungry issue in personalized product search. We find that data-hungry issue exists under the few-shot setting caused by personalization, and degrades the performance under the few-shot setting when the input query consists of diverse intents. Furthermore, we illustrate that with such a data-hungry issue, the returned search results tend to be close to the products the user purchases most often, or the products the most users purchase in the market given the same query. The result in the further experiment confirms our conclusions.