You always need to look at the obvious first. The path with least resistance. Stem plants ALWAYS rot from the bottom up, without forming roots, when there is not enough light. Always. Nitrate and other nutients will not make any difference at all if there is not bright enough light. Light comes first. If you have between 2 and 3 watts of flourescent light per gallon of water then light is not the issue, unless you are only running it for 2 hours a day! If you are under 2 watts per gallon then light IS the issue. Pretty simple.
And last, roots shooting off from the stem generally indicates a deficiency of one of your macro nutrients, N, P,or K.
Not nessasarily. If light is weak the stem portion in the substrate will rot while higher up on the stem where it is closer to the light it may send out roots. If you then cut off the rotted portion and re plant the stem with the aireal root, it will just happen all over again