Following recent policy changes by X (Twitter) and other social media platforms, user interaction data has become increasingly difficult to access. These restrictions are impeding robust research pertaining to social and political phenomena online, which is critical due to the profound impact social media platforms may have on our societies. Here, we investigate the reliability of polarization measures obtained from different samples of social media data by studying the structural polarization of the Polish political debate on Twitter over a 24-hour period. First, we show that the political discussion on Twitter is only a small subset of the wider Twitter discussion. Second, we find that large samples can be representative of the whole political discussion on a platform, but small samples consistently fail to accurately reflect the true structure of polarization online. Finally, we demonstrate that keyword-based samples can be representative if keywords are selected with great care, but that poorly selected keywords can result in substantial political bias in the sampled data. Our findings demonstrate that it is not possible to measure polarization in a reliable way with small, sampled datasets, highlighting why the current lack of research data is so problematic, and providing insight into the practical implementation of the European Union's Digital Service Act which aims to improve researchers' access to social media data.