ABSTRACT Numerous eruptive variable young stellar objects (YSOs), mostly Class I systems, were recently detected by the near-infrared Vista Variables in the Via Lactea (VVV) survey. We present an exploratory near-infrared spectroscopic variability study of 14 eruptive YSOs. The variations were sampled over one-day and one-to-two-year intervals and analysed in combination with VVV light curves. CO overtone absorption features are observed on three objects with FUor-like spectra: all show deeper absorption when they are brighter. This implies stronger emission from the circumstellar disc with a steeper vertical temperature gradient when the accretion rate is higher. This confirms the nature of fast VVV FUor-like events, in line with the accepted picture for classical FUors. The absence of Brγ emission in a FUor-like object declining to pre-outburst brightness suggests that reconstruction of the stellar magnetic field is a slow process. Within the one-day time-scale, 60 per cent of H2-emitting YSOs show significant but modest variation, and 2/6 sources have large variations in Brγ. Over year-long time-scales, H2 flux variations remain modest despite up to 1.8 mag variation in Ks. This indicates that emission from the molecular outflow usually arises further from the protostar and is unaffected by relatively large changes in accretion rate on year-long time-scales. Two objects show signs of on/off magnetospheric accretion traced by Brγ emission. In addition, a 60 per cent inter-night brightening of the H2 outflow is detected in one YSO.