This work investigates Artificial Intelligence (AI) systems that detect respiratory insufficiency (RI) by analyzing speech audios, thus treating speech as a RI biomarker. Previous works collected RI data (P1) from COVID-19 patients during the first phase of the pandemic and trained modern AI models, such as CNNs and Transformers, which achieved $96.5\%$ accuracy, showing the feasibility of RI detection via AI. Here, we collect RI patient data (P2) with several causes besides COVID-19, aiming at extending AI-based RI detection. We also collected control data from hospital patients without RI. We show that the considered models, when trained on P1, do not generalize to P2, indicating that COVID-19 RI has features that may not be found in all RI types.