R-22 Flight Instructor reported while training autorotation's needing to take control of the aircraft as they loss control of the aircraft. Flight Instructor recovered the aircraft and returned to their base.

Narrative

I was training a student on autorotation's. It was there first lesson so I start with autorotative glides. After our 8th glide I decided to head back to base. On the way back I told my student lets do one more and choose a spot. So we entered the autorotation and on the glide down I was teaching what they were doing wrong and how to fix it. As we started our recovery to climb out I had to fix what the student was learning. So as I got the altitude and airspeed back under control and the engine rolled back on I realized the auto was terminated too late. I recovered and climbed on my way back to base without an issue. I explained what happened and why and how we recover. And how autorotation are a fast and precise maneuver that can get close for comfort in training. I believe the cause of the problem which was misjudgment was due to fatigue. Since I have done many autorotation's in the past with no miscalculations on recovery. So I decided to prioritize getting more sleep; canceling or teaching ground if I feel any less than 100%; and no more than 3 autorotation's per lesson. So I will only be performing autorotation's in the morning when I am most alert and prioritizing teaching the basics of flight as the evening comes along.