We examine evidence for communicative intent during conspecific interactions in wild chimpanzees (Budongo Forest, Uganda), focusing on persistence in gestural communication. Previous research indicates that great apes have large gestural repertoires and produce gestural communication in a flexible and intentional manner, including the production of gesture sequences. Although there is a lack of consensus on the form and function of sequences, there is some evidence that sequences are produced when signallers fail to receive any response from a recipient. Here, we provide first systematic evidence for communicative persistence in wild chimpanzees. Rather than examining only the presence or absence of a response, we used the most commonly observed response to assign meanings to gestures and examined sequence production in relation to response congruency. Chimpanzees ceased communication if successful, but persevered when unsuccessful. Chimpanzees repeated gestures when a response partially matched their goal but substituted the original gesture when a response was incongruent. Persistence was also mediated by recipient intent to respond, with more sequences produced within competitive than affiliative contexts. Gestures within sequences were homogenous in semantic meaning and signallers continued until the response matched the assigned meaning of the initial gesture. Gestural sequence production was not primarily affective; gesture intensity (in terms of modality) did not increase within sequences. Chimpanzee gestural sequences emerged to achieve specific outcomes; given variability in recipient behaviour following initial gestures, signallers were flexible in their persistence towards these goals.