The dependence of the measured damping rate (gamma/omega) on the value of the safety factor on axis (q(0)) and of the toroidal rotation shear has been experimentally determined for n = 1 toroidal Alfven eigenmodes (TAEs) in JET limiter plasmas with a monotonic safety factor profile and low edge magnetic shear. For q(0) < 1, the n = 1 TAE damping rate can reach values up to (gamma/omega) > 8%, whereas for q(0) > 1.1, gamma/omega) < 2% for similar experimental conditions. The existence of these two separate regimes is suggestive of a possible role of the sawteeth on the damping of low-n TAEs, for example, via a redistribution of the core plasma current, which would, in turn, affect the magnetic shear profile. The value of the toroidal rotation shear affects the n = 1 TAE damping rate only at high neutral beam injection power (P-NBI): for PNBI > 6.5 MW we find that gamma/omega > 2% in plasmas with a higher rotation shear, whereas for lower PNBI we do not observe any appreciable effect of the rotation shear on the damping rate. These observations indicate that different damping mechanisms for low-n TAEs may be active at low and high performance.