I always assumed cyberzombies drained astral energy because they could no longer generate their own aura.
Borrowing some terminology from Mage: The Ascension here. Everybody has a Pattern (Essense) that they naturally filter astral energy through. The form that the energy feeds through the Pattern is what gives you your aura. Since no two people have the same Pattern, no two people can have the same aura (unless you magically modify it).
Mages have Patterns that are more maleable then most, allowing them to modify the raw astral energies at a fundamental level. You could look at it as while humans have "screen door" patterns Mages have large holes in that screen that lets the mana flow unimpeded.
Cyberzombies no longer have a functioning Pattern and cannot filter astral energies anymore. Without this energy the spirit cannot survive and thus it tries to take off. Without the spirit the body cannot operate - it malfunctions like a car going 100mph without a driver. The cyberzombies spirit is locked into the body (it may not be fooled but actually FORCED to stay). But it cannot survive without a Pattern. So one of the nasty things the cybermancers do is create an artificial Pattern. Essentially a spell matrix that absorbs astral energy and feeds it to the spirit.
Obviously if you have sub-zero essense you're no longer feeding mana into the enviroment like everyone else. So the farther "in the hole" you are the more energy the matrix/Pattern has to draw from the surrounding area to keep your spirit locked up.