Word for energyless-ness
Solution 1:
Exhaustion: the state of being exhausted.
Where exhausted is the state of having used all of someone's mental or physical energy : to be tired out or worn out (someone) completely; to be completely used up.
Exhaustion has the meaning of being completely "energyless", whereas words like lethargy and fatigue more closely mean "having little energy".
Solution 2:
Depending on the context, "Lethargy" may be a fit.
http://m.dictionary.com/definition/lethargy
Similarly there is: "sluggishness", "listlessness", "lassitude" and "fatigue".
Surely one of these will fit.
UPDATE:
In light of clarifications, FATIGUE is the word you seek.
http://m.dictionary.com/definition/fatigue
Solution 3:
To emphasize the lack of energy, use exhaustion. To emphasize the effort that led to exhaustion, use fatigue. For a more informal term, you can use burnout.
Solution 4:
If someone is losing energy that would imply that they do have some energy remaining. However if you want to convey total exhaustion, you could use the word, "spent".
Solution 5:
drained would be suitable.
to exhaust physically or emotionally < feeling drained at the end of a long workday >