We investigate the crustal magnetic signatures of lunar craters using Lunar Prospector (LP) electron reflectometer data. Craters of all ages often have associated magnetic lows, showing that crustal fields were present even in pre-Nectarian times (≳3.9 Ga). Magnetic lows extend to ~2--4 crater radii, suggesting shock rather than thermal demagnetization. Younger craters are more likely to have clear and complete demagnetization signatures, suggesting that many older magnetic lows have been subsequently obscured. No size dependence is found for craters larger than 50 km in diameter, suggesting that demagnetization effects for all craters in this size range completely penetrate the magnetized layer. If shock demagnetization is responsible, this suggests an upper limit of ~50 km for the depth of magnetization. Evidence of edge effects due to magnetization contrasts may show that strong far-side crustal fields are coherent at scales of ~25 km.