Just like on a non e-bike, depending on rider weight, ability, accessories, tire pressure, length of hill, angle or grade of hill, etc., you will be able to climb some and others you will not.
If your motor stops receiving power on the same or similar type of hill twice, please avoid those for your next few rides and see how the bike performs. If it is not having any issues, then that hill is likely beyond the combined ability of you and the bike.
The PAS will stop providing assist if there is too much resistance for the motor. Also, there is overheat protection for the controller.
Each of the Avadar ebikes come with a geared hub motor in the rear wheel. The gearing provides some mechanical advantage and can assist you up many hills. Keyword, being assist. You should always be pedaling when climbing a hill, get a running start, and make sure you are in the best gear for that hill. You also want to be in the best PAS, which will often be the highest. In addition, you can engage the throttle while pedaling with PAS on to provide maximum power to the motor while climbing.
Choosing the right gear:
If it is kind of steep or the rider needs the mechanical advantage, the lowest gear will be the best gear. This allows the pedals to spin fast and the rider to generate power to assist the motor. Low gear, or 1st gear will be the largest cog on the rear wheel.
If the hill is not really steep, but definitely not flat, a slightly higher gear may be best. If you can maintain some speed in the pedals after shifting up, that gear will probably work. If you shift up again, and the pedals are moving too slowly around, then it will be difficult for you to generate the force required in this gear and you should probably down shift for this hill or only up shift after gaining more speed in the lower gear.
Choosing the right PAS (And how that relates to AMPS).
If you are on a longer hill, that is not necessarily steep, you could still over heat the controller or motor if the rider is too tired to pedal hard enough to provide enough assist. In this situation, using a slightly lower PAS or limiting your AMPS in your display settings, may improve your ability to continue riding this hill in the future. This will also lower the amount of Amps being sent to the motor. In general, the more amps sent, the faster something can over heat. By adjusting to one of the lower settings, you will reduce the amount of amps being sent to the motor during this prolonged climb.
In summary, if you are repeatedly experiencing no power to the motor after climbing a specific hill or similar hill, it is likely this hill is beyond the ability of the combination of the rider and ebike. There are limits, if this happens, unfortunately, it would be best to find a different path or place to ride.
At a minimum, if your motor stops receiving power on the same or similar type of hill twice, please avoid those for your next few rides and see how the bike performs. If it is not having any issues, then that hill is likely beyond the combined ability of you and the bike.
Over time, as you ride more, you may find you can revisit some hills you could not previously ride if your fitness and endurance has increased and you are looking for a workout.