The motor or transaxil lock up and stop the

It is likely to be an overheating issue, or a motor overload. There is some help in the link but it likely needs dealer service and the motors themselves may need lubricating or even replacing Correct diagnosis is the key to problems like this.

https://www.google.com/search?q=Quingo+plus+suddenly+stops

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Some scooters are fitted with an electric safety brake which engages when the power is off.

While there could be a mechanical fault with the transmission or motor this would seem unlikely as when the fault is absent the scooter presumably runs ok.

It would seem the electric brake is engaging either due to a fault in the brake or because of an interruption in the power supply to it. That might mean the battery but unlikely. That would be fairly obvious as the complete machine would die at the same time it stopped and you made no mention of that.

your problem is related to the overload breaker on the chair you need to figure out why the breaker is tripping either due to batteries going bad or the brushes in the motor need adjusting or replaced , also you need to check the automatic brake is releasing completly a dragging brake will cause the auto reset breaker to trip

If your brakes are locking up while driving, this is a serious issue and you should stop driving the scooter and contact a technician. You can do very serious damage to your equipment that can result in replacing the motor, transaxle and/or both.

to push start a motor bike you have to use a higher gear like third gear but if you are only pushing it from one place to another then it is better in neutral or out of gear

I believe that is a safety for if your on an incline you do not just free wheel uncontrollably. But that is not a 100% answer

If your batteries are running very low, this is the most likely source of your problems. 80% of my scooter repairs involve batteries. The fact that your scooter runs is a good thing. The fact that it runs only a few feet and gives you no error code when it stops indicates the electronics have no battery power to indicate a flash code. The back wheels jamming probably relates to a no power condition causing the brake to lock (it takes power to release the brake and turn the motor)
This scooter uses two U-1 batteries that last between 1 and 2 years. From your description, I would replace the batteries first and make any further determination of any problems, if any,after that. These batteries are available locally at a large discount (between $50 and $160 each) and can be installed with basic tools, saving you money on the labor charge.
Shop around for the best price. Charge the new batteries fully before use. Enjoy.
Hope this helps.

This could be caused by a couple of different issues. If your batteries fall to below 17 volts the unit will shut down. After it sets for a few minutes it may run again for a short time. If this is the case, then the batteries are not being charged properly or they are not holding charge.
Another cause could be the break switch circuit is opening. If that is the case, replace the brake/motor harness

Hi. 8 flashes is a fault code for a motor fault. It will be either worn brushes in the motor or faulty connectors to the motor. This fault code means that there is no circuit through the motor. Probably time to overhaul the motor. Most mobility scooters have plugs and sockets that are really to small to carry the amount of current that they do. Because of this, they sometimes fail.Good luck. Neil.