Healthcare applications may have strict availability requirements, such that system failures can affect patient monitoring. Therefore, a failure may lead to serious problems regarding patient health. This paper presents an approach for assessing the availability of healthcare Internet of Things (IoT) systems using Reliability Block Diagrams (RBD). A case study is presented for a hospital environment, in which patients are under constant observation. A sensitivity analysis is also carried out to identify the most influential components, and, then, we propose mechanisms to mitigate the impact of component failure.