Quasi-periodic eruptions (QPEs) are enigmatic high amplitude bursts of X-ray radiation with a recurrence period of a few to several hours, recently discovered near the central supermassive black holes (SMBHs) of a few distant galaxies [1-3]. The periodic flares are naturally explained by a star on an eccentric orbit, shedding mass at each pericenter passage, resulting in a highly-modulated accretion luminosity. The energetics of each eruption indicate accretion of roughly 1e-7 M_sun and therefore an apparent evolution time of ~5000 years for a solar mass donor. Assuming stable mass transfer driven by the emission of gravitational waves, the mass-losing object must be a dense stellar object (white dwarf or Helium star) on a highly eccentric (e>0.95) orbit [4,5]. However, these objects are rare since emission of gravitational waves tends to circularize orbits. This led to the suggestion of more complicated scenarios involving two interacting stars on coplanar, counter-rotating orbits , or star-disk collisions . Here we argue that QPEs are produced by a main-sequence star orbiting a SMBH on a mildly eccentric orbit (e~0.1). By relaxing the assumption of stable mass transfer, we break the equality between the gravitational wave timescale and the apparent evolution timescale, and therefore infer almost circular orbits which are more frequent. The unstable mass transfer implies that the observed QPEs will evolve within the next ~10 years - they will significantly brighten, and then cease to flare. This timescale is much shorter than the apparent lifetime, allowing for observational test of our predictions. Indeed, archival data of one QPE system shows that it was dimmer two decades ago . We show that a combination of two body scattering and gravitational wave emission around SMBHs produces roughly 10^-6 yr-1 gal-1 stars on orbits that generate QPEs. Given our calculated lifetime of ~10 years, we obtain an abundance of order 1e-5 gal-1 consistent with the eROSITA blind QPE search .