We present deep Giant Metrewave Radio Telescope (GMRT) radio observations at 240, 330 and 610 MHz of the complex radio source at the center of the NGC1407 galaxy group. Previous GMRT observations at 240 MHz revealed faint, diffuse emission enclosing the central twin-jet radio galaxy. This has been interpreted as an indication of two possible radio outbursts occurring at different times. Both the inner double and diffuse component are detected in the new GMRT images at high levels of significance. Combining the GMRT observations with archival Very Large Array data at 1.4 and 4.9 GHz, we derive the total spectrum of both components. The inner double has a spectral index \alpha=0.7, typical for active, extended radio galaxies, whereas the spectrum of the large-scale emission is very steep, with \alpha=1.8 between 240 MHz and 1.4 GHz. The radiative age of the large-scale component is very long, ~300 Myr, compared to ~30 Myr estimated for the central double, confirming that the diffuse component was generated during a former cycle of activity of the central galaxy. The current activity have so far released an energy which is nearly one order of magnitude lower than that associated with the former outburst. The group X-ray emission in the Chandra and XMM-Newton images and extended radio emission show a similar swept-back morphology. We speculate that the two structures are both affected by the motion of the group core, perhaps due to the core sloshing in response to a recent encounter with the nearby elliptical galaxy NGC1400.