I haven't slept more than 4 consecutive hours over the course of the past couple weeks, and the results are: not catastrophic.
Here's a fun side-effect of having a puppy about the house: I haven't slept for more than 4 continuous hours in a couple of weeks.
Puppies have almost zero bladder control, which means that even if he wanted to (& I'm not convinced that he does), Ghyll isn't able to hold it until we get up in the morning. For which reason I get up twice in the night—at 1:00 and at 4:00—to take him outside for a few minutes, coerce him into doing his business, and put him back to bed. Sam and I have arrived at this arrangement mostly out of my inability to cope with his early morning breakfast-related high energy. He's usually up for an hour from 7:30 to 8:30 and then back to napping until 10:30 or so.
So far I don't think I'm experiencing any catastrophic effects. I think that sailboat racing crews tend to operate on short shifts where they sleep polyphasically throughout the day; and apparently most humans in Western civilisation slept biphasically (that is, waking once for a couple hours in the middle of the night) before the Industrial Revolution allowed us to stay up well past sunset. That being said, I don't think that racing crews sleep like that on shore; and pre-industrial biphasic sleep took place over like 12 hours of darkness, whereas I'm fitting my schedule into the regular old 8 hours. The takeaway is that it's not going to kill me—but preliminary results indicate that it's not doing my long-term memory consolidation any favours.