We report here on the longest deep X–ray observation of a supergiant fast X–ray transient ( SFXT ) outside outburst , with an average luminosity level of 10 ^ { 33 } erg s ^ { -1 } ( assuming 3 kpc distance ) . This observation was performed with Suzaku in December 2009 and was targeted on IGR J08408–4503 , with a net exposure with the X–ray imaging spectrometer ( XIS , 0.4–10 keV ) and the hard X–ray detector ( HXD , 15–100 keV ) of 67.4 ks and 64.7 ks , respectively , spanning about three days . The source was caught in a low intensity state characterized by an initially average X–ray luminosity level of 4 \times 10 ^ { 32 } erg s ^ { -1 } ( 0.5-10 keV ) during the first 120 ks , followed by two long flares ( about 45 ks each ) peaking at a flux a factor of about 3 higher than the initial pre-flare emission . Both XIS spectra ( initial emission and the two subsequent long flares ) can be fitted with a double component spectrum , with a soft thermal plasma model together with a power law , differently absorbed . The spectral characteristics suggest that the source is accreting matter even at this very low intensity level . From the HXD observation we place an upper limit of 6 \times 10 ^ { 33 } erg s ^ { -1 } ( 15–40 keV ; 3 kpc distance ) to the hard X–ray emission , which is the most stringent constraint on the hard X–ray emission during a low intensity state in a SFXT , to date . The timescale observed for the two low intensity long flares is indicative of an orbital separation of the order of 10 ^ { 13 } cm in IGR J08408–4503 .