For the main part of people covered by a supplementary health insurance (SHI) contract, reimbursements are lower than contributions, revealing an “insurance gap”. The magnitude and the persistence of this insurance gap may fuel the decision of the SHI policy holder either to opt out or to switch for another level of coverage. This empirical work focuses on decision by the insured to retain or discontinue their SHI policy with the help of duration models estimated on data from 216,114 individuals insured by one of the main French SHI providers (MGEN) over the 2011-2020 period. We found evidence that the insurance gap plays a significant role in the opting-out decision for a specific population of insured: people who are not working, who are students, single, young, without children or those who formerly chose a low level of coverage appear be more sensitive to this insurance gap, causing them to leave. In addition, the requirement for employers to offer group contracts to their employees starting in 2016 (Accord National Interprofessionnel, ANI) seems to have had an important impact on individual decisions to leave their SHI policy.