We examine the melt rheology of a series of ethylene-methacrylic acid (E/MAA) ionomers, all based on the same E/MAA copolymer, with an emphasis on the low-shear-rate Newtonian region. All ionomers show Newtonian behavior at sufficiently low shear rates. The zero-shear viscosity eta(0) is a strong function of neutralization level and is significantly higher for Zn ionomers than for Na ionomers at the temperatures and neutralization levels examined. The recoverable compliance J(e)(0) is independent of cation type and neutralization level, indicating that the ionic associations bear no stress during steady flow in the terminal region. Therefore, the individual ionic associations have lifetimes much shorter than the terminal relaxation time of the polymer chain. We probe the effect of unneutralized acid groups on eta(0) by removing these groups through esterification. Unneutralized acid groups substantially lower the viscosity of Na ionomers but have no discernable effect in Zn ionomers. An "acid-cation exchange" mechanism is proposed to explain these findings.