We first investigate in natural time the numerical simulations of a simple deterministic self-organized critical system introduced to describe avalanches in stick-slip phenomena. It is one-dimensional and belongs to the same universality class as the train model for earthquakes introduced by Burridge and Knopoff. We show that the variance κ1=χ2−χ2 of natural time χ, becomes approximately equal to 0.070 when the system approaches the critical state. Next, we analyze in natural time the small earthquakes subsequent to the low-frequency magnetic-field precursor observed near the epicenter of the Ms7.1 Loma Prieta earthquake in 1989. We find that almost five days before the mainshock, the condition κ1≈0.070 was reached.