Well, I can say that every once in a while I go through phases where this sort of thing can happen. At one point I jokingly said that I should sleep in half lotus at nightime!
Anyways, from my own experience...
It's not always possible, but better to try not to practice right before bed if you are kind of tired. I also began trying to become aware of the point where I was starting to loose focus and beginning to dri..
...Oh! Sorry! (a little "sleepy" humor
).. and beginning to drift off. This seemed to help, as I was able to catch myself quickly and regain focus.
You could try when you wake up. I did for a short while, still, I'm more of an evening person.
There was a short time that it became a little frustrating to me, and perhaps this didn't help. Once I took the "shrug your shoulders" approach, sort of saying to myself "go ahead, fall asleep!", it was not really an issue anymore. Go figure. (actually this is sort of like the first line from the text that retro quoted, of not giving much thought to "not wanting to fall asleep".)
One other thing I have done in the passed is remembering bodhicitta, and thinking that I am practicing for the benefit of all sentient beings. I do not want to let them down, so therefore I will try to fight off this mental laxity and focus.
On the other hand, there are a few occasions where I was very lethargic during meditation, and once that passed there was a sudden very sharp alertness and focus for the remainder.
Don't know if this helps but...