Chronic obstructive pulmonary disease (COPD) is a serious inflammatory lung disease affecting millions of people around the world. Due to an obstructed airflow from the lungs, it also becomes manifest in patients' vocal behaviour. Of particular importance is the detection of an exacerbation episode, which marks an acute phase and often requires hospitalisation and treatment. Previous work has shown that it is possible to distinguish between a pre- and a post-treatment state using automatic analysis of read speech. In this contribution, we examine whether sustained vowels can provide a complementary lens for telling apart these two states. Using a cohort of 50 patients, we show that the inclusion of sustained vowels can improve performance to up to 79\% unweighted average recall, from a 71\% baseline using read speech. We further identify and interpret the most important acoustic features that characterise the manifestation of COPD in sustained vowels.