I think there are a couple things to consider.
Our son was born while I was working at a startup. In my opinion, for the first few months, I was definitely functioning with less sleep than ever before. The regular 8 became a broken 6, just as you say, but I felt fresh in the mornings and didn't nod off during the afternoon. Basically, I felt "normal." I don't know if it's adrenaline or some other biological phenomenon, but something was super-charging my energy level.
But eventually this began to change. I noticed because of specific things that seemed out of the ordinary: More bugs were creeping into my code (I know this from objective measurements); I fell asleep and missed my train stop (first time ever); I started making comments that I later regretted (more than usual). Eventually, I started adding these things up and realized I was no longer functioning at the level I expected.
My suggestion is to watch for warning signs, such as the ones I saw. Look for patterns throughout your life. It won't affect only work, but also your relationships, family, recreation, everything.
What to do about it? That's different for everyone. You can reset your expectations. You can reduce the amount of stuff you try to do each day/week/month. You can power through it. You can make some life changes. It's going to be different for everyone. Anyone else have suggestions?