Public health authorities and political leaders need to come across as trustworthy in their handling of a crisis like the COVID-19 pandemic. There is, however, little knowledge about how the affordances and dynamics of social media influence perceptions of trustworthiness, especially during a protracted crisis. In this article, we study how Twitter users were discussing the trustworthiness of the Norwegian health authorities and political leadership throughout three periods of partial lockdown during the COVID-19 pandemic. Across all the periods, there was a substantial number of positive comments, but these were outweighed by negative ones. Ability was clearly the most discussed factor for trustworthiness, and many users offered up their lay expertise. Discussions of integrity and benevolence were less frequent and mostly negative when they occurred. An increase in negative comments during the last period might be read as an expression of fatigue, and there was a noted dissatisfaction with the ability of the political leadership. Taken together, the study suggests Twitter to be an arena where users are exposed to arguments and counterarguments in negotiations over ability in particular. Such discussions can intensify as a crisis drags on and are important to grasp for health authorities and political leadership alike. Thus, the study sheds light on the contribution that a socio-technical platform like Twitter makes to the discursive formation of trustworthiness over time, which in turn might function to strengthen or erode public trust in public authorities and political leadership.