What kind of plane? And does that matter? My CFI told me when he was checking me out in the club 182 that these planes aren’t trainers and it’s not good for them to be doing tight pattern work with repetitive t&g’s. He would suggest going out to the local VOR and come back with goal to cruise a bit more. Or go airport hopping.
That’s silly. If you need takeoff and landing work in a 182, do it. Plowing along in cruise isn’t going to fix bad landings.
Anyway... to the OP’s question...
Most students shut down as they fatigue and aren’t learning anything new anyway after some point in time. Whether that’s 20 minutes, 40 minutes, an hour, or two, isn’t really the measuring stick. Whether or not they’re still focused and learning is.
There’s SOME value in doing a FEW landings a bit fatigued because someday you’ll have a long long day on a trip and you’ll arrive at the destination a tad too tired than you should have allowed yourself to be, and the unforecast heavy gusting crosswind will have arrived five minutes before you got there. So yeah. You need a little bit of practice in how to wake yourself up, and get yourself fully focused for the task at hand.
But generally, if you’re fatigued you’re not learning anything anyway. You’re probably just repeating the same mistakes over and over. Park it and call it a day.
Additionally, the comments about using full stop taxi-backs or stop and goes where runway distance permits and you’re comfortable with the engine out options at the departure end, are solid. Not because they’ll help with fatigue, but you have time to think and process between each landing more.
If you’re really working out a landing slump or problem, stopping and taxiing back and maybe even making yourself talk out loud through the last landing and analyzing it, maybe even using the extra time to keep a little scoresheet on your knee board with stuff like “airspeed” “directional control” “control placement after touchdown” etc, can show a pattern problem or show improvement to help keep your head in the game.
Making anything into a game can get the thinking side of your brain interested instead of just plodding through the motions by rote and letting the brain wander off thinking about other things.
Heck, bet yourself things. “If I can get this down and stopped with a short field landing by X, I can call it quits and I get to go have a Coke from the fridge.” Whatever floats your boat.
If you hit a point where you’ve run out of ideas to keep it interesting and can’t see any improvement, you’re saturated or distracted. Call it. Or do something to wake yourself back up. Like
@midlifeflyer said, maybe head to a nearby different airport to change up the sight picture. Something.
Otherwise, if you’re not focused and interested, you’re already done, you just haven’t taxied in yet. Park it.
I’ve gone out to do a few landings and work on something and two landings in I decided my brain wasn’t in it today, and called it quits.
I’ve also had two hour marathons doing power off 180s picking different spots, forcing different configurations of the aircraft (instead of letting the flight path dictate them, example, full flaps from start to finish) where everything was firing on all cylinders and I was progressing and enjoying it. (Only a few days of that total though, those are butt kicker sessions because you WILL be worn out after a solid workout like that.)
Whether to call it or keep working on something specific is really practice in assessing your own state of alertness, focus, goal-setting, and skill progression. That applies for pattern work as well as any other training or proficiency flying.
I’m sure the aerobatics folk here who practice for competition or just proficiency agree... some days you’re just not up to the game. Other days, a long session results in a lot of progress or even some epiphany about your techniques or common mistakes that you can use to fix it forever.
