When does the cotyledon die on a marijuana plant?

The reason the Cotyledon (rounded, small leaves at the very bottom of the stem) is because the roots of the marijuana plant are growing more, and it is just natural for these to wither and fall off. Do not panic when this happens.

On a further note, add more soil up to where the Cotyledon are, or as close as you can to the first set of the jagged "true" leaves of the plant. This will help growth.