Social media platforms are constantly shifting towards algorithmically curated content based on implicit or explicit user feedback. Regulators, as well as researchers, are calling for systematic social media algorithmic audits as this shift leads to enclosing users in filter bubbles and leading them to more problematic content. An important aspect of such audits is the reproducibility and generalisability of their findings, as it allows to draw verifiable conclusions and audit potential changes in algorithms over time. In this work, we study the reproducibility of the existing sockpuppeting audits of TikTok recommender systems, and the generalizability of their findings. In our efforts to reproduce the previous works, we find multiple challenges stemming from social media platform changes and content evolution, but also the research works themselves. These drawbacks limit the audit reproducibility and require an extensive effort altogether with inevitable adjustments to the auditing methodology. Our experiments also reveal that these one-shot audit findings often hold only in the short term, implying that the reproducibility and generalizability of the audits heavily depend on the methodological choices and the state of algorithms and content on the platform. This highlights the importance of reproducible audits that allow us to determine how the situation changes in time.