A minute? Wow, you better tell us what you're telling yourself in that one minute because I think you've stumbled upon the cure for insomnia.
If entering the accelerated learning state, we at first spend a couple of minutes just relaxing. If you're zoning out at that point. Get more sleep you obviously need it. Since falling asleep at that point usually happens to the sleep deprived.
The other reason you might be falling asleep within the minute, you're allowing yourself to be bored and letting the mind wander off.
Make sure you're sitting upright and sit a little more to the front edge of the seat. Don't use the backrest. As soon as you hit that nice relaxed focused state, say your affirmations and move on.
Once you've done it a few times 3 in and out breaths will be enough to state your intent and purpose and start flipping pages.
Alex