People in receipt of pre-exposure prophylaxis (PrEP) for the prevention of HIV in Sub-Saharan Africa often discontinue taking the medication. We conducted 27 semi-structured interviews with men and women who had started PrEP but did not return to the clinic for a refill after a 1, 2 or 3-month period. These 'discontinuation' clients were enrolled in a PrEP demonstration project for the general population in nurse-led, public-sector, primary-care clinics in Eswatini. Reasons for discontinuation included changes to self-perceived HIV risk such as the end of pregnancy and absent partners. Others described PrEP as inaccessible when working away from home and many described difficulties relating to a daily pill regimen and managing side effects. Female clients described being prohibited from using PrEP by their partners and co-wives. From these results, we recommend that client-centred counselling stresses the prevention-effective adherence paradigm, which promotes PrEP use in risk periods that are identifiable and PrEP discontinuation when the risk period has finished. A national scale up of PrEP may mitigate problems accessing PrEP. Extended counselling and support could assist with adherence and the management of side effects. Education and support for partners and families of PrEP clients may also contribute to better PrEP continuation.