ABSTRACT During thermonuclear bursts, it is suspected that cooling of the corona by the burst emission may be the cause of hard X-ray deficits. Although such a deficit has been observed in nine sources, it has not been observed from 4U 1608–52, a nearby prolific burster. Therefore, the authenticity and universality of the hard X-ray deficit may be in question. To investigate this suspicion, Insight–HXMT performed cadence observations during the low/hard state of 4U 1608–52 in 2022 September and detected 10 thermonuclear X-ray bursts. Two of these bursts show a double-peaked structure in the soft X-ray band, which could be caused by the high temperature of the burst emission and a marginal photospheric radius expansion (PRE) around the burst peak time. This is indicated by their peak fluxes being up to the Eddington limit and having a large colour factor at the peak of the bursts. A hard X-ray deficit is observed at a significant level during bursts at > 30 keV. Furthermore, the fraction of this deficit shows saturation at 50 per cent for the first eight bursts. This saturation may indicate that the corona is layered and only part of the corona is cooled by the bursts: for example, the part close to the neutron star surface is cooled while the rest remains intact during bursts. This result provides a clue to the geometry of the corona. For example, a possible scenario is that the corona has two forms: a quasi-spheric corona between the neutron star and the disc and a disc corona on both surfaces of the disc.