Doing the impossible and making it look easy can be fun, but like many have said, it's a bad idea to make a practice of doing.
Besides the health and safety problems, which are fairly obvious, you're also setting an expectation that you are their slave and are willing to do inhuman things to accomplish what their lack of planning and unrealistic timeline goals can not. Driving while sleep deprived is on par with drunk driving by the way.
In my experience, this type of practice tends to make clients and partners undervalue you.
It's a very rare occurrence, usually mandated by client contracts to others or outages, that would require this kind of effort. I only do this kind of thing when things are on fire and I'm the only metaphorical fireman on site.
Normally I would adviceadvise taking an appropriate amount of padding in the assignment/project to allow for it to be done professionally instead of a madcap nosleep endurance dash that could have embarrassing artifacts produced in the midst of a sleep-dep walking sleepzombie state.
So yes. This is not normal, nor should it be considered normal. Even if you don't realize it, you'll be hitting diminishing returns after about a day. You will achieve more with a properly focused and regimented schedule.