You raise a couple of interesting aspects of what's going on, fatigue being one, but also the stress level. In some of these cases, like Ms. Donaldson was describing, the trial goes on for months or years. Jurors become bored. The first thing you learn when you observe a jury trial is it's not at all like the jury trials on TV; in fact, they're really tedious, even ones that are sensationalized cases. The manner in which attorneys are required to phrase their questions and how the evidence is presented can drag on and on. It's not unusual to see jurors sleeping, at least in American trials. In longer trials, jurors are clearly not paying attention for long periods of time. If they're allowed to have their phones with them, they're on their phones, so many courts now require them to leave the phones in the jury room so they can't do that. Fatigue and boredom are going to work against the ability to process the information, pretty much in the way you'd expect.
The issue of jurors being upset by what is going on is a little trickier, because to some extent that increases their ability to pay attention. If they become more alert because they're shown some interesting pictures of the crime scene, or what have you, they might pay attention a little more. However, that can reach a point where their anxiety level becomes so pronounced that it makes it harder for them to pay attention, or they're paying attention to aspects of it that might not be legally appropriate, so it can become prejudicial in some of those cases as well. We would describe that as an inverted U-shaped function, to use technical language. Up to a point, maintaining interest and having some sort of arousal level can be beneficial, but then past a point it can be counterproductive.