The fact that you're getting even brief naps is very good, but Evo is right: tell your doctor. I don't know what your illness is, but if we're talking about an infection of some kind, remember that sleep is (probably) crucial to the maintenance of your immune system.
Anyway, to directly answer you: unless exhaustion becomes part of a larger crash, then it's an issue. Generally, people will become so exhausted that they'll begin to "lose time", and experience cat-naps while apparently awake: that would be your second BIG warning sign.
The warning sign you need to be aware of, that will be your bell-weather in the world of sleep deprivation, are 2 classes of hallucinations.
The first are... first... and appear to be dark (often brown) spots or blobs just at the corners of the vision, racing out of the field of vision. The second, far more worrying, is the perception of insects on or in the skin, and is a sign that there is damage beginning to occur in the brain.
In terms of actually living through this?... not the issue: unless you have a grave illness of a peculiar type, this won't kill you directly. It DOES put you at a far greater risk for muscular and connective tissue injuries, and other injury while driving or even during normal activity. Over time, generally around the 7 day mark, you begin to do irreversible damage to your brain that gets ugly very quickly, and eventually people essentially begin to experience REM while appearing awake and...
paranoia
psychosis
fatal cardiac event (especially arrhythmia)
damage to the hippocampus and probably a lot more
coma
death
So... yeah, get some sleep, but 72, or even 96 hours will make you miserable beyond belief, but it won't kill you. Stay hydrated, stay safe, and contact your GP or an ER if this persists: you need sleep to live, and brain chemistry is variable; don't take risks on when you'll start to do lasting damage.