Does heavy lifting tire out your nervous system?

Short answer

The nerves do tire, but muscle is the main cause. After heavy squats, the ability to fully drive the muscle stayed lower for 48 hours, but the muscle's own force was also lower for 48 hours, and nerve responses did not differ between 3-rep and 12-rep weights. What slowed recovery more was not the weight but sets taken to failure.

Does heavy lifting tire out your nervous system?
'Heavy weights → nerve fatigue → days of rest': does this formula hold?
A common claim is that heavy lifting tires the nervous system (the brain and spinal cord) before the muscles, so you need days of rest. We checked how large and how long nerve fatigue is, separately from muscle fatigue.
What happens to the nerves after heavy squats?
The muscle was driven less fully for 48 hours
10 people did 10 sets of 5 squats at 80% of their maximum. The brain's ability to fully drive the muscle stayed lower for 48 hours. The muscle's own force was also lower for 48 hours, and overall fatigue cleared after 72 hours.
But muscle was the center of the fatigue
The nerve signal dropped for 10 minutes, muscle force for over 20 minutes
In the same study there were no other nerve changes, and the researchers concluded that the fatigue did not come mainly from the nerves. In a study where 16 people repeated efforts at 85% of maximum force until failure, the drop in nerve signal (9%) recovered within 10 minutes, while the drop in the muscle's own force (15%) remained after 20 minutes.
Do heavier weights tire the nerves more?
3-rep and 12-rep weights: no difference in nerve responses
When 14 people did 5 sets with a weight they could lift only 3 times and 3 sets with a weight they could lift 12 times, nerve measures taken up to 72 hours did not differ between the two. In a 16-person study, only the heavy session reduced muscle drive right afterwards, but after 1 hour both sessions showed slightly reduced drive, while overall recovery was nearly complete.
What slowed recovery was going to failure
Even at the same volume, failure added 24-48 hours
When 10 people compared 3 sets of 10 to failure with 6 sets of 5 (same volume) using a 10-rep weight, recovery after the failure sets was 24-48 hours slower. In a 24-person bench press trial, bar speed right after dropped 25% when going to failure, 13% when leaving 1 rep, and 8% when leaving 3 reps.
Speed was back within 48 hours
3% difference at 24 hours, none at 48 hours
At 24 hours, those 24 people were 3% slower after failure or 1 rep left, and 2% faster after 3 reps left. At 48 hours the three approaches did not differ. In another study where 10 people trained to failure, performance measures returned within 48 hours, but feeling recovered and soreness lagged even at 48 hours.
Summary: nerves tire too, but muscle is the main cause
Same muscle every 48-72 hours, leave about 3 reps per set
There was some drop on the nerve side, but muscle was the center of the fatigue, and heavier weights did not make nerve fatigue last longer. What slowed recovery was taking sets to failure. When training the same muscle heavy again, waiting 48-72 hours and leaving about 3 reps per set is enough.