Measuring and inferring the key physical parameters of jets in active galactic nuclei (AGN) requires high-resolution very long baseline interferometry (VLBI) observations. Using VLBI to measure a core-shift effect is a common way of obtaining estimates of the jet magnetic field strength, a key parameter for understanding jet physics. The VLBI core is typically identified as the bright feature at the upstream end of the jet, and the position of this feature changes with the observed frequency, rcore ∝ ν−1/kr. Due to the variable nature of AGN, flares can cause variability of the measured core shift. In this work, we investigated the time variability of the core-shift effect in the luminous blazar 3C 454.3. We employed a self-referencing analysis of multi-frequency (5, 8, 15, 22−24, and 43 GHz) Very Long Baseline Array (VLBA) data covering 19 epochs from 2005 to 2010. We found significant core-shift variability ranging from 0.27 to 0.86 milliarcsec between 5 GHz and 43 GHz. These results confirm the core-shift variability phenomenon observed previously. Furthermore, we also found time variability of the core-shift index, kr, which was typically below one, with an average value of 0.85 ± 0.08 and a standard deviation of 0.30. Values of kr below one were found during flaring and quiescent states. Our results indicate that the commonly assumed conical jet shape and equipartition conditions do not always hold simultaneously. Even so, these conditions are typically assumed when deriving magnetic field strengths from core-shift measurements, which can lead to unreliable results if kr significantly deviates from unity. Therefore, it is necessary to verify that kr = 1 actually holds before using core-shift measurements and the equipartition assumption to derive physical conditions in the jets. When kr = 1 epochs are selected in the case of 3C 454.3, the magnetic field estimates are consistent, even though the core shift varies significantly with time. Subsequently, we estimated the magnetic flux in the jet of 3C 454.3 and found that the source is in the magnetically arrested disc state, which agrees with earlier studies. Finally, we found a good correlation of the core position with the core flux density, rcore ∝ Score0.7, which is consistent with increased particle density during the flares.