You're getting down to the biology of muscle contraction. You can read up on the sliding filament model, which is really quite interesting. Basically your muscles contract because of chemical reactions (temporarily chemically altering your cells). Ca2+ (calcium) is used heavily in the process, and it gets depleted. The more force your muscles need to produce, the more calcium they'll use up.
Related to your bench press example, your muscles are chemically using less ingredients in order to push the bar up with less weight. When you start asking for a lot of it (heavy weights) in a short period of time (more reps) you cause it to use more more muscular fuel (ATP, calcium, etc). You also are causing physical fiber damage routinely to your muscles when pushing them hard so you are mechanically weaker.
There are other things too, which might even matter more. Decreased serotonin, which can happen after long exercise, can lower your neural effectiveness at firing muscles (a.k.a. "cns fatigue"). Maybe there's plenty of calcium, but now it's a serotonin thing.