Pushing to failer is so so misunderstood.
Failer during training (not talking a P/L meet attempt, just training the muscles) is when ever you need to take a brake from your set tempo during a set. IT'S NOT when you can't even even move it.
When you take the brake and take the tention off the target muscle weather it is at a lock out or full eccentric position of the muscle, your muscle and CNS start to recover. Thats why even with a few sec brake, you can push more reps after the brake.
You took a break, you failed at that point. Admit it and move on. You just hit your goal.