We report on a broad-band X-ray study (0.5-250 keV) of the Supergiant Fast X-ray Transient IGR J18483-0311 using archival INTEGRAL data and a new targeted XMM-Newton observation. Our INTEGRAL investigation discovered for the first time an unusually long X-ray activity (3-60 keV) which continuously lasted for at least 11 days, i.e. a significant fraction (about 60%) of the entire orbital period, and spanned orbital phases corresponding to both periastron and apastron passages. This prolongated X-ray activity is at odds with the much shorter durations marking outbursts from classical SFXTs especially above 20 keV, as such it represents a departure from their nominal behavior and it adds a further extreme characteristic to the already extreme SFXT IGR J18483-0311. Our IBIS/ISGRI high energy investigation (100-250 keV) of archival outbursts activity from the source showed that the recently reported hint of a possible hard X-ray tail is not real and it is likely due to noisy background. The new XMM-Newton targeted observation did not detect any sign of strong X-ray outburst activity from the source despite being performed close to its periastron passage, on the contrary IGR J18483-0311 was caught during the common intermediate X-ray state with a low luminosity value of 3x10^33 erg s^-1 (0.5-10 keV). We discuss all the reported results in the framework of both spherically symmetric clumpy wind scenario and quasi-spherical settling accretion model.