I am of two minds on this issue. I think that in most situations, the polite thing to do as a passenger is to remain awake.
I have to admit being a tad annoyed with my friend who fell asleep during the entire drive to a bridal shower a couple of hours away. We both had to get up early for the trip, and I understand that she was tired (and I am one of those lucky people who never get sleepy while driving, regardless of how tired I am). However, I was bored and would have loved some conversation. Plus, I had never been to the party location before and I was hoping she would be the navigator, but since she was sleeping I had to read the directions and drive at the same time, which makes me nervous.
On the other hand, I was the offender in a far more egregious situation. A friend drove him and me to a white-water-rafting trip organized by another friend who had experience with such trips. The day started very early getting there (meaning it was dark for the first 2 hours of the trip, and I did stay awake for that portion), and then once we got there, we spent 10 hours navigating the course (we were doing a two-day trip in one day). Then we all went to a diner for dinner. After that my driver friend and I took off for home. It was cold out (and had been so all day) so the heat was blasting in the car to warm us up. I was exhausted, as I do not usually physically exert myself for 10 hours straight. Between the heat, my exhaustion, and the big meal, I just could not keep my eyes open no matter how hard I tried. I donít think Iíve ever been so absolutely compelled to sleep as I was then. I still feel terrible that my friend had to drive back basically alone while I slept, but I donít know what else I could have done at the time.
So for the OP, I think if she tries to stay awake but canít, thatís all she can reasonably be expected to do.