I used to work a swing swift. Pretty much experience sleep deprivation for 20 yrs. Two evenings, quick turnaround to two days, then a mid shift. At the end of the week your sleep would be messed up and it would take the days off to get back to normal then you'd start all over again. The quick turn around with 8 hrs between shifts would start the sleep deprivation or mess your sleep habits up, the fourth day would be an early shift, like 6am to 2pm, then go back in 8 hours later to work the mid. Try to get a few hours before the mid and maybe get some on the mid. If you got some sleep on the mid you could stay up the next day but end up going to sleep early evening.
There was a time I'd get off the 4th day, not get any sleep, go in on the mid, maybe get 2-3 hrs sleep, then stay up the next day til normal time to go to bed. So that's like staying up 36-40 hrs with 3 hrs sleep. The mind doesn't function too well after about mid day but physically not too bad. The next day your biorhythm would be messed up so the body/mind would shut down about middle of the day. The day after that would be close to normal. Then you'd start all over again.
So I'd say the 36-40 hours with 2-3 hrs sleep could be a limit. The scary part was when you woke up after staying up such a long period, you lose complete sense of time when you do wake up and it takes a few minutes to get your bearings. For me anyway.