If I leave my computer running indefinitely, it quickly becomes "psychologically exhausted", runs slowly, starts causing programs to crash, and so on.

• really? Oh you mean if you kept using it, not if you just left it there? I would suspect that the equivalent (and this is a stretched analogy, but let's go with it) would be that a human brain would "fill up" with memories. But over what timescale? The amount of genuinely "new" experiences that a human has probably already varies by 1-2 orders of magnitude. Do people with particularly exciting lives full of new careers/hobbies/travel/goals/relationships go insane after 20 years? No... I mean maybe they would after 1000 years. But that's my point: the timescale for psychological "exhaustion" will be hugely varied. We kind of already know that it is.