Question: I have noticed that when I find myself sleep deprived my singing voice gets greatly impaired. It is difficult to reach and sustain higher notes and it's like my voice muscles are "sore". 

I guess that's a given, considering I'm tired, but I wanted to know what are the implications of these less than optimal nights in my voice. Should I avoid singing in this kind of situation? Can this permanently damage my voice? Can this be corrected by posterior well rested nights?

Answer: 
One word: Severely.

Of all the musicians in a group, the singer must be the most concerned about getting enough sleep. And the older you get, the more important this becomes.

You should also be concerned about staying hydrated, meaning: drink a lot of water. Be careful with alcohol or caffeine or smoking, all of which can fatigue the voice due to depriving the mouth and larynx of moisture, leading to fatigue and strain when you sing.

If you have had too little sleep and too little hydration, and you sing anyway, you will increase the likelihood of straining and injuring your voice by singing. So if there is a day that you have not had enough sleep, try to sing less and talk less also.

If you develop severe voice problems, the first thing a doctor will tell you is to stop singing and talking for a week, a month, or longer, and to stop rehearsing and performing until you have healed. You do not want to let things get that bad.

Some people are more prone to vocal problems than others. Simply be mindful of how you feel each day, and figure out what you should do to protect your voice from unnecessary strain. But of course you must also practice singing to keep your voice strong. You are like an athlete; you want to keep your physical training up, but you do not want to risk injury from too much exertion.

Your voice must last your entire life, so if you are serious about singing your best, be mindful of all the advice on this page.
All depends on the person. There are singers that can go go go, and others that whisper during the day to save their voice. Look at Celine Dion in comparison to Steve Perry.