If you’ve ever lifted weights, you’ll know what I mean.
Let’s say a bench press regimen consists of 3 sets, 250 lbs for each set and the lifter tries to do as many presses as possible each set. Also, let’s assume that the lifter takes a two minute break between sets.
If I tried this, what would happen is I’d do the most presses the first set, fewer the second, and still fewer for the third.
What is the physiological mechanism underlying this type of fatigue?
Have you already ruled out lactic acid buildup in the muscles? It doesn’t seem, under the circumstances you describe, that there would be sufficient oxygen supplied to the muscles during exertion, or sufficient time for the buildup to be to be dealt with, to prevent aches related to this.
I think that if you waited longer between sets you would find that you could do more reps (although probably not your maximum) per set.
I would guess that lactic acid wouldn’t be the main factor due to the waiting period between reps. For arguments sake, lets say I wait 10 minutes. The same phenomenon is observed.
My guess, and this is just a guess, is that it has to do with nerve impulses that enervate the muscles. If you’ve worked a set with the number of repetitions to exhaustion, the ions necessary to do more have been depleted. If you begin another set before the ions have been fully restored, they will be depleted at a smaller number of reps.
I just want to add that calcium (which is in ion form) is very important for muscle contraction. That will take longer to replace than sodium and potassium, the main two ions (called electrolytes) involved in muscle enervation.
A lack of Wheaties. 
There’s probably a few things going on, but the reduction of ATP and/or creatine in the muscle cells is probably a major factor. ATP is the primary fuel system in brief, high-intensity activities like bench presses. As the “P” (phosphate) in ATP gets used up, the muscles recharge it with creatine-phosphate, which was stored locally in the muscle. When ATP can no longer be recharged fast enough, your energy dwindles. Restoring creatine back to optimum levels probably takes a few days.
Like barbitu8 said, there’s other factors involved too.
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“Forgive your enemies, but never forget their names.” – John F. Kennedy
** LAO TZU ** That’s probably the reason that creatine is supposed to be a good supplement for quick energy bursts, such as weight lifting. Also quick speed work, such as intervals.