We examine the implications of including a paleomagnetic field on sputtering loss of argon and neon from the Martian atmosphere. In a previous investigation <Hutchins and Jakosky, 1996>, we found that collisional sputtering from the exobase by oxygen pickup ions dramatically modified the evolution of atmospheric argon and neon (removing greater than 85% of outgassed 36Ar over time and the present atmospheric allotment of 20Ne in <100 Myr) and could easily reproduce the anomalous isotopic fractionation of 36Ar/38Ar. However, the existence of an intrinsic magnetic field could limit sputtering loss by deflecting the solar wind around the upper atmosphere, reducing the number of oxygen pickup ions produced. Evaluation of argon and neon atmospheric evolution including a magnetic field results in lower sputtering loss rates if the magnetic field shut off between 2.5 and 3.6 Gyr. Nonetheless, the extent of sputtering loss requires atmospheric input from sources, in addition to outgassing by intrusive and extrusive volcanism, capable of providing 4--100 times more argon and 40--1800 times more neon (than provided by volcanic outgassing), dependent on the time that sputtering begins. The additional volatile source(s) must also preferentially outgas neon relative to argon by a factor of between 10 and 26.¿ 1997 American Geophysical Union