Speaking English is one of the most challenging skills for English as a Foreign Language (EFL) students, and many now practice independently through artificial intelligence (AI) speech evaluation systems outside the classroom in Informal Digital Learning of English (IDLE) contexts. To sustain practice that does not always go smoothly, perseverance of effort, one component of grit, is required. However, previous studies on grit and IDLE in EFL contexts have predominantly used quantitative or mixed-methods approaches, offering limited insight into how perseverance of effort is experienced and demonstrated by learners, particularly Indonesian EFL university students in AI-IDLE contexts. This study addresses this gap by exploring how EFL students demonstrate perseverance of effort when facing challenges while using Moodie.ai for speaking practice and identifying the aspects that contribute to their perseverance. Using narrative inquiry, the study involved three EFL university students in Surakarta, Indonesia, through in-depth interviews. The findings revealed that participants faced technical issues, difficulty understanding the platform's features and feedback, language limitations, emotional pressure, and time-management challenges. Nevertheless, they continued practicing through repetition, gradual adjustments, and the use of feedback. Their perseverance of effort appeared not as overflowing enthusiasm but as small, repeated actions from one session to the next. This perseverance was supported by individual reasons, experiences with the technology, and contextual factors, particularly academic demands. However, once their academic obligations ended, the participants did not continue using Moodie.ai independently, suggesting that their motivation was more extrinsic than intrinsic.