Sleep studies have shown that some people ideally need only 5-6 hours of sleep while others needed 9+ regularly to feel rested and energetic throughout their days. The average was found to be 8 hours.
Direct muscle recovery isn't a major issue during sleep, but central nervous system and immune system recovery and support are. Deprive yourself of adequate sleep for too long, and you run a greater risk of having a poor workout here and there on one end of the spectrum to serious CNS overtraining on the other. And it's a bitch that CNS overtraining can manifest itself through stubborn insomnia when you do finally get the time to sleep. Sleep deprivation also makes one more prone to coming down sick with flu bugs and what not as sleep plays a significant role in immunofunction support.
If you have no alternative to a stressful, sleep-depriving schedule, then some things you can do are:
1. Short power naps (even in your car on breaks, if need be)
2. Short sessions of meditation have been shown to be beneficial for CNS and immune system support
3. Make sure you're getting you're getting good nutrition including enough anti-oxidants
4. Relax/extend your goals (for example, say your goal is to gain X amount of muscle or add X amount of weight to a lift over 3 months, you might revise that goal to gain that amount of muscle or weight over 4-6 months instead)
5. Consider adding an extra rest day or two into your workout split if you can