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. Threshold and stiffness have been identified and compared with linear and non-linear predictions of the gyro-kinetic code GS2. Comparison of plasmas with different values of toroidal rotation indicates a significant increase in R/LTi in rotating plasmas. Various experimental 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 critical value, 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.