Left pedal keeps falling off - Stamina Products Stamina 1305 Indoor Cycle Exercise Bike

Remove the pedal, clean the threads on both parts. Put Red Loctite on the threads and torque it down. Leave 24 hours before use.

You need to clean the threads and use this.

Loctite® Threadlocker Red 271™

https://www.loctiteproducts.com > ... > Specialty Glues
Loctite Threadlocker Red 271 is designed to lock and seal threaded fasteners permanently and prevent loosening from vibration. Ideal for fasteners up to 1" .

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Just my thoughts.
If the treads are stripped are warn on the pedal or inside the arm. The threads in the arm may need to be tapped or the threads on the shaft need to be rethreaded to clean the threads.
Could be the bearing in the pedal is not turning free and as you pedal the bike it is unscrewing the pedal from the arm.
After you tighten the pedal shaft to the arm the pedal should turn freely on the shaft and not bind.

use lock tight

Try using "locktite" thread lock to help keep it from loosening. U can buy it at automotive or hardware stores.
Or use fingernail polish on the threads as a cheap substitute

Btw, I’m available to help over the phone in case u need at https://www.6ya.com/expert/jan_ed8272c8c2968d14

YOU MAYBE HAVING AN ISSUE WITH THE SPROCKETS THAT HOLD THE DRIVE CHAINS ON BOTH PEDALS. YOU CAN PURCHASE THEM SEPARATELY OR A COMPLETE HUB ASSEMBLY. TO REACH STAIRMASTER/NAUTILUS @ 1-800-864-1270

Change the screw or huddle hardly the screw.

i have the stairmaster 4000pt which was bought new in 2003. in 2007, i started experiencing the same problem, the right pedal would sometime slip and fall to the floor. i called the local fitness store and they came and replaced the hub assembly and that resolved the problem until now. The left pedal is now slipping.

We had the same problem with the right pedal continually falling off. I purchased some "J.B. Weld" from Ace Hardware, applied it to the stud on the pedal, re-tightened it back on the sprocket arm and let it set 24 hours. This was over a month ago and it has not come off or loose. It gets peddled pretty furiously at times and still holds. The cost of the J.B. Weld which is in two small tubes, mixed together and applied is less than $7.00. I am once again my Grand-daughters hero....

You need a new crank arm. If you ride with the nut loosened what happens is the square part of the bottom bracket shaft wears the hole out in the aluminum crank and it no longer fits snugly no matter how much you tighten it down.