During their formation phase stars gain most of their mass in violent episodic accretion events, such as observed in FU Orionis (FUor) and EXor stars. V346 Normae is a well-studied FUor that underwent a strong outburst beginning in $sim1980$. Here, we report photometric and spectroscopic observations which show that the visual/near-infrared brightness has decreased dramatically between the 1990s and 2010 (${Delta}Rapprox10.9^{rm m}$, ${Delta}Japprox7.8^{rm m}$, ${Delta}Kapprox5.8^{rm m}$). The spectral properties of this fading event cannot be explained with variable extinction alone, but indicate a drop in accretion rate by 2-3 orders of magnitude, marking the first time that a member of the FUor class has been observed to switch to a very low accretion phase. Remarkably, in the last few years (2011-2015) V346 Nor has brightened again at all near-infrared wavelengths, indicating the onset of a new outburst event. The observed behaviour might be consistent with the clustered luminosity bursts that have been predicted by recent gravitational instability and fragmentation models for the early stages of protostellar evolution. Given V346 Nors unique characteristics (concerning outburst duration, repetition frequency, and spectroscopic diagnostics), our results also highlight the need for revisiting the FUor/EXor classification scheme.