Chagas disease (CD) is a neglected tropical disease caused by Trypanosoma cruzi infection that, despite being discovered over a century ago, remains a public health problem, mainly in developing countries. Since T. cruzi can infect a wide range of mammalian host cells, parasite–host interactions may be critical to infection outcome. The intense immune stimulation that helps the control of the parasite’s replication and dissemination may also be linked with the pathogenesis and symptomatology worsening. Here, we discuss the findings that support the notion that excessive immune system stimulation driven by parasite persistence might elicit a progressive loss and collapse of immune functions. In this context, cellular stress and inflammatory responses elicited by T. cruzi induce fibroblast and other immune cell senescence phenotypes that may compromise the host’s capacity to control the magnitude of T. cruzi-induced inflammation, contributing to parasite persistence and CD progression. A better understanding of the steps involved in the induction of this chronic inflammatory status, which disables host defense capacity, providing an extra advantage to the parasite and predisposing infected hosts prematurely to immunosenescence, may provide insights to designing and developing novel therapeutic approaches to prevent and treat Chagas disease.