‘Every Earthquake a Precursor According to Scale’ (EEPAS) is a model to forecast earthquakes within the coming months, years and decades, depending on magnitude. EEPAS performs well for seismically active regions including New Zealand (NZ) and has been formally evaluated in Collaboratory for the Study of Earthquake Predictability (CSEP) centres in NZ and California, USA. It has been used for practical forecasting in NZ for nearly a decade. An EEPAS forecast is formed by accumulating the contributions from past earthquakes to the expectation of future earthquakes. It uses the precursory scale increase (Ψ) phenomenon along with three predictive spatial, temporal and magnitude scaling relations. For a particular mainshock, Ψ is identified as a prior sharp increase in the occurrence of minor earthquakes. Each identification is represented by a value of precursor magnitude MP, precursor time TP and precursory area AP. An algorithm to automatically identify Ψ was developed and applied to real and synthetic earthquake catalogs. Multiple identifications of Ψ were obtained for most mainshocks. A trade-off between AP and TP was observed among such multiple identifications. Here, we examine the implications of the trade-off for the EEPAS temporal and spatial scaling parameters aT and σA. The EEPAS parameters were initially fitted to the NZ earthquake catalog from 1986-2006. The EEPAS parameters are now refitted with a sequence of fixed values for aT and then for σA. The range of fixed values constrain the respective temporal and spatial scales to vary by a factor of a hundred. Results confirm the existence of a similar space-time trade-off in EEPAS as in Ψ, with large aT values being associated with small σA values and vice versa. We conclude that the space-time trade-off is an intrinsic feature of precursory seismicity. This exists independently of other influences, such as the local strain rate, that may contribute to scatter in the predictive scaling relations. Mixing EEPAS models with parameters along the trade-off line should improve forecasting.