Warning, my answer is going to be very boring: 24 hours was the maximum for me. I just love sleeping and I hate feeling tired.
On that particular day I was at a big rock concert and because of the rain, our tent got flooded and we had to leave earlier. This was the longest journey home I have ever experienced in my life. My eyes kept falling shut, my mood went below the from-here-you-better-watch-out-mark, my head hurt, my brain hurt, my legs hurt, I was hungry, grumpy, tired, tired, tired and oh so tired. I hated every second of it.
Since then I have always made sure that I grab some sleep, even if it is just 10 minutes here and there. Having been in a full time rock band I know what sleep deprivation means. I trained power napping and after a few months I was able to fall asleep instantly, everywhere.
Yoiur 'Team Leader'