I have noticed that if I start a live session at night (where I had no sleep of any kind for the last 12 hours) that initially my level of concentration may start off perfectly acceptably. However, I noticed various levels of degredation within a few hours. The first thing that I will notice is that sometimes on the turn or river I will have forgotten my exact hand that I mucked preflop. Additionally, I may have forgotten the exact sequence of play on earlier betting rounds (e.g. who raised or reraised preflop).
These types of things don't matter so much when playing online because of hand histories. In live play, I think they are a warning sign that my fatigue factor will soon exceed acceptable levels (unless the game is really good, meaning that the poor play of the opponents more than compensates for my diminished capacities). Once I start forgetting my hand while I am still involved in the hand, that is pretty much it for me.
When I'm considering whether or not to start an online session, I will sometimes ask my spouse to toss me a small object like a candy from across the room. I won't go nuts trying to catch it. I casually reach out for it, and if I can't make the catch, then it is no go on the session.