Here's a couple links to stories describing studies about decision fatigue:
The gist is, judges are more likely to be receptive to an argument early in the day or right after a food break. The theory is that we wear down and get grumpier over time, and that it's just harder to keep making decision after decision over time. The impact of this problem manifests in lots of ways, notably with diets. Because you have to make many, many decisions over the day not to stuff yourself, as the day wears on, the ability to exercise your will power erodes. Hence the frequency of the diet-buster midnight snack.
So what do we do about this phenomenon? We can't control where we are in the order of an argument list, so when we find ourselves last in the string before the First Circuit, we can't very well hand the panel snicker bars and tell them to take a break before they hear our appeal.
With diets, they say the key is to minimize having to exercise will power. Take all the bad food out of the house, walk to work on the street without the donut shop, etc. But judges have a set of decisions to make and they can't really make fewer of them.
One thing we can all do is be more aware and sensitive to this pressure. So whenever you are making a decision, whether a lawyer crafting a brief or the judge deciding which way to go, sleep on it. You can write that brief into the wee hours, but schedule yourself so you aren't having to hit the ECF button that night. Make sure you have the time to re-visit and ponder the next day, when you are fresh.
Similarly, pace yourself. Judges, it appears from these studies, should avoid having to make too many decisions in a day. If they have to hear a cluster of arguments at once, they should take lots of breaks, nibbling away on healthy things and do jumping jacks during those breaks.
When I was grading masses of bar exams, I took a number of steps to try to strip out unconscious influences - I graded everything with someone else, so I had another perspective; I didn't try to do it in marathon sessions; and I reviewed every answer multiple times, mixing up the order of my review (you will be affected by the quality of the answer you read before the next answer). And throughout this process, I used a key for identifying the elements of the proper answer.
The truth is that you aren't going to have any idea what sort of outside influences are moving on your judge. The judge may not be aware of some of them. We do the best job we can and hope for the best. I suppose the most we can say is if we see we are last on the list, we have to do whatever we can to try to bring some energy into the court room, to wake everybody up. While it's always a good idea to be snappy, if it's been a long day for the judge, it's especially important to CUT TO THE CHASE, and do whatever you can to invite questions and make the judge engage.
Humans are not computers. That's a good thing. But it also means we have to recognize and do what we can to keep the upside of human decision-making without the down side.