We present the discovery and characterization of six new M dwarf eclipsing binary systems. The 12 stars in these eclipsing systems have masses spanning 0.38-0.59M_{sun}_ and orbital periods of 0.6-1.7 days, with typical uncertainties of ~0.3% in mass and ~0.5%-2.0% in radius. Combined with six known systems with high-precision measurements, our results reveal an intriguing trend in the low-mass regime. For stars with M=0.35-0.80M_{sun}_, components in short-period binary systems (P<~1 day; 12 stars) have radii which are inflated by up to 10% ({mu}=4.8+/-1.0%) with respect to evolutionary models for low-mass main-sequence stars, whereas components in longer-period systems (>1.5 days; 12 stars) tend to have smaller radii ({mu}=1.7+/-0.7%).