We present the evolution of the X-ray emission properties of the magnetar 1E 1547.0–5408 since February 2004 over a time period covering three outbursts. We analyzed new and archival observations taken with the Swift, NuSTAR, Chandra, and XMM–Newton X-ray satellites. The source has been observed at a relatively steady soft X-ray flux of ≈10⁻¹¹ erg cm⁻² s⁻¹ (0.3–10 keV) over the last 9 years, which is about an order of magnitude fainter than the flux at the peak of the last outburst in 2009, but a factor of ∼30 larger than the level in 2006. The broad-band spectrum extracted from two recent NuSTAR observations in April 2016 and February 2019 showed a faint hard X-ray emission up to ∼70 keV. Its spectrum is adequately described by a flat power law component, and its flux is ∼7 × 10⁻¹² erg cm⁻² s⁻¹ (10–70 keV), that is a factor of ∼20 smaller than at the peak of the 2009 outburst. The hard X-ray spectral shape has flattened significantly in time, which is at variance with the overall cooling trend of the soft X-ray component. The pulse profile extracted from these NuSTAR pointings displays variability in shape and amplitude with energy (up to ≈25 keV). Our analysis shows that the flux of 1E 1547.0–5408 is not yet decaying to the 2006 level and that the source has been lingering in a stable, high-intensity state for several years. This might suggest that magnetars can hop among distinct persistent states that are probably connected to outburst episodes and that their persistent thermal emission can be almost entirely powered by the dissipation of currents in the corona.