The magnetic signatures and crater retention ages of the 19 largest (>1000 km diameter) impact basins on Mars are examined to constrain the history of the acquisition of crustal magnetization during the Noachian era. The 5 most clearly impact-demagnetized basins are younger than the 14 basins within which lies substantially re-magnetized crust. Poisson analysis shows that the most likely time of this magnetization cessation was 4.115-4.13 Ga (model age) and that it occurred quickly, taking less than 20 Ma. A global decrease in effective crustal magnetic susceptibility due, e.g., to a decrease in the rate of hydrothermal alteration, is one possible explanation. Alternatively, the cessation of post-impact magnetization reflects the rapid death of the Martian dynamo.