In Gurbani Amrit Vela is described at the second "phaar" of the day, there are 8 phaars (divisions) of the day.
1st Phaar is 12 am to 3am
2nd Phaar is 3 am to 6 am and so on.
Reasoning behind this as described by Bhai Vir Singh Ji in his book called Jap Ji Sahib, is that at this time Maya has put her full intoxication into affect and that most people are deep in slumber due to her intoxication. Those awake at this time who have fought the first battle of the day and woke up are those that try to progress in this cycle of life and death. And those that have merged back into Waheguru are awake at this time as well (mentally) and there Vichars (thoughts) help those on the path.
Now i've stated that but you gotta remember this is on a spiritual level. There are those people that work at this time and some that are travelling on planes and stuff. So the situation is different for them. Take me for example i used to from 3 am to 11 am at UPS. I would be up at 2 am get ready and go to work and i would to my nitnem while i was at work. The greatest thing about Sikhism is that for each situation it is has different answer. FLEXABILITY! No other religion has this. Most are hardcore rules and regulations ie time to eat, pray, sleep, clothing,
But in the end. If you can't wake up its not like its a totally bad thing. But we must put the effort in. Saying that it will effect your body is only an excuse a person uses so he doesn't even start the battle.
Start the battle almost 90% of the time you'll lose but one day when Kirpa happen you'll see the Anand of Amrit Vela.