Fatigue and/or dyspnea on exertion (DOE) result in immobility (a relative decrease in mobility), which leads to deconditioning, which then leads to more fatigue and/or DOE.
I believe we can handle these loops with DAGs by considering how the events are occurring across time, and the state of the system being studied across time (which clearly changes). So the above could be considered as a DAG across three iterations (changes in state over time):
Here we see the same consequences, but the models explicitly recognizes the changes in state over time. Which, I believe, can be a helpful aspect of using DAGs in the modeling of the causal processes at play in a clinical scenario. After all, to get back to the initial state a patient must traverse each state along the way, unless there are jumps in state. If we can anchor the states with other variables that would then change over time we can consider how far, and by what path someone may return to a previous level of functions.
In summary, the fact the DAGs are acyclic does not provide a barrier to their use as representations of clinical practice knowledge, but rather an opportunity to consider the cycles we commonly refer to as they play out over time and the state of the system change over time.