Context. Supergiant fast X-ray transients (SFXTs) are high mass X-ray binaries (HMXBs) that are characterised by a hard X-ray (≥ 15 keV) flaring behaviour. These flares reach peak luminosities of 10 36 -10 37 erg s −1 and last a few hours in the hard X-rays. Aims. We investigate the long-term properties of SFXTs by examining the soft (0.3−10 keV) X-ray emission of the three least active SFXTs in the hard X-ray and by comparing them with the remainder of the SFXT sample. Methods. We performed the first high-sensitivity soft X-ray long-term monitoring with Swift/XRT of three relatively unexplored SFXTs, IGR J08408−4503, IGR J16328−4726, and IGR J16465−4507, whose hard X-ray duty cycles are the lowest measured among the SFXT sample. We assessed how long each source spends in each flux state and compared their properties with those of the prototypical SFXTs.Results. The behaviour of IGR J08408−4503 and IGR J16328−4726 resembles that of other SFXTs, and it is characterised by a relatively high inactivity duty cycle (IDC) and pronounced dynamic range (DR) in the X-ray luminosity. We found DR ∼ 7400, IDC ∼ 67% for IGR J08408−4503, and DR ∼ 750, IDC ∼ 61% for IGR J16328−4726 (in all cases the IDC is given with respect to the limiting flux sensitivity of XRT, that is 1−3 × 10 −12 erg cm −2 s −1 ). In common with all the most extreme SFXT prototypes (IGR J17544−2619, XTE J1739−302, and IGR J16479−4514), IGR J08408−4503 shows two distinct flare populations. The first one is associated with the brightest outbursts (X-ray luminosity L X 10 35−36 erg s −1 ), while the second comprises dimmer events with typical luminosities of L X 10 35 erg s −1 . This double-peaked distribution of the flares as a function of the X-ray luminosity seems to be a ubiquitous feature of the extreme SFXTs. The lower DR of IGR J16328−4726 suggests that this is an intermediate SFXT. IGR J16465−4507 is characterised by a low IDC ∼ 5% and a relatively narrow DR ∼ 40, reminiscent of classical supergiant HMXBs. The duty cycles measured with XRT are found to be comparable with those reported previously by BAT and INTEGRAL, when the higher limiting sensitivities of these instruments are taken into account and sufficiently long observational campaigns are available. By making use of these new results and those we reported previously, we prove that no clear correlation exists between the duty cycles of the SFXTs and their orbital periods. Conclusions. The unique sensitivity and scheduling flexibility of Swift/XRT allowed us to carry out an efficient long-term monitoring of the SFXTs, following their activity across more than 4 orders of magnitude in X-ray luminosity. While it is not possible to exclude that particular distributions of the clump and wind parameters may produce double-peaked differential distributions in the X-ray luminosities of the SFXTs, the lack of a clear correlation between the duty cycles and orbital periods of these sources make it difficult to interpret their peculiar variability by only using arguments related to the properti...