Experiments have been carried out in the JET tokamak in order to determine the critical ion temperature inverse gradient length (R/LTi = R|Ti|/Ti) for the onset of Ion Temperature Gradient modes and the stiffness of Ti profiles with respect to deviations from the critical value. The existence of a threshold in R/LTi has been assessed and its value found in close agreement with linear GS2 gyro-kinetic calculations. The ion stiffness level is high and keeps R/LTi close to the linear threshold irrespective of the amount of core ion heating. This finding is not in agreement with non-linear GS2 calculations, yielding significantly higher R/LTi values than the linear threshold. Comparison of plasmas with different values of toroidal rotation indicates a significant increase in R/LTi in rotating plasmas. Various observations allow to conclude that such increase is mainly due to a decrease of the stiffness level with increasing rotation, rather than to a mere up-shift of the threshold, as commonly predicted by theory. This finding has implications on the interpretation of present day experimental results on the effect of rotation on confinement as well as on extrapolations to future machines.