The dependence of the measured damping rate (γ/ω) upon the value of the safety factor on axis (q0) and of the toroidal rotation shear has been experimentally determined for n=1 Toroidal Alfvén Eigenmodes (TAEs) in JET limiter plasmas with a monotonic safety factor profile and low edge magnetic shear. For q0<1 the n=1 TAE damping rate can reach values up to γ/ω>8%, whereas for q0>1.1 γ/ω<2% for similar experimental conditions. The transition between these two regimes provides an empirical indication of a possible role of the sawteeth in redistributing the plasma current, hence affecting the damping of low-n TAEs through a different magnetic shear profile. The value of the toroidal rotation shear affects the n=1 TAE damping rate only at high Neutral Beam Injection power (PNBI): for PNBI>6.5MW we that γ/ω>2% in plasmas with higher rotation shear, whereas for lower PNBI we do not observe any appreciable effect of the rotation shear on γ/ω. These observations indicate that different damping mechanisms for low-n TAEs may be active at low and high performance, prompting further detailed theoretical modelling.