© 2017 The Authors. We examine the stability of feedback-regulated star formation (SF) in galactic nuclei and contrast it to SF in extended discs. In galactic nuclei, the orbital time becomes shorter than the time over which feedback from young stars evolves. We argue analytically that traditional feedback-regulated SF equilibrium models break down in the regime. We study this using numerical simulations with the pc-scale resolution and explicit stellar feedback taken from stellar evolution models. The nuclear gas mass, young stellar mass and star formation rate (SFR) within the central ~100 pc (the short-time-scale regime) never reach steady state, but instead go through dramatic, oscillatory cycles. Stars form until a critical surface density of young stars is present (where feedback overwhelms gravity), at which point they expel gas from the nucleus. Since the dynamical times are shorter than the stellar evolution times, the stars do not die as the gas is expelled, but continue to push, triggering a runaway quenching of SF in the nucleus. However, the expelled gas is largely not unbound from the galaxy, but goes into a galactic fountain that re-fills the nuclear region after the massive stars from the previous burst cycle have died off (~50-Myr time-scale). On large scales ( > 1 kpc), the galaxy-scale gas content and SFR is more stable.We examine the consequences of this episodic nuclear SF for the Kennicutt-Schmidt (KS) relation: While a tight KS relation exists on ~1-kpc scales, the scatter increases dramatically in smaller apertures centred on galactic nuclei.