The capability of showing affective expressions is important for the design of social robots in many contexts, where the robot is designed to communicate with humans. It is reasonable to expect that, similar to all other interaction modalities, communicating with affective expressions is not without limitations. In this paper, we present two online video studies (72 and 50 participants) and investigate if/to what extent the recognition of affective displays of a zoomorphic robot is affected under situations with different levels of visibility. Recognition of five affective expressions under five visibility effects were studied. The intensity of the effects was more pronounced in the second experiment. While visual constraints affected recognition of expressions, our results showed that affective displays of the robot conveyed through its head and body motions can be robust and recognition rates can still be high even under severe visibility constraints. This study supported the effectiveness of using affective displays as a complementary communication modality in human-robot interaction in situations with visibility constraints, e.g. in the case of older users with visual impairments, or in outdoor scenarios such as search-and-rescue.