@Wolf krannich
This is why electrical problems are not much fun! What Joe is saying makes sense, and it is only one piece of the puzzle, the LVC in the controller.
For the good news, if you can get 8-9 ah out of a 10 ah battery, that's fine. You want the LVC to stop pulling out of the battery at around that point. The key, right now, is how to get that 85% discharge. You should be able to just plug the charger into the 'empty' battery and get a full charge, without multiple cycles on the charger.
The Watts Up doesn't draw much. You can see what is happening if you turn on the battery system, on the bike, with no power being drawn from the motor. The circuitry will have a small draw. Any bad connection can leak power or prevent current from flowing. I solder everything, and use good connectors.
I agree with you on the temperatures. It would need to be colder for any real impacts, and batteries get warm when you draw them down.
There are a lot of things that change in the first six months. New riders get used to using the motor, they tend to go faster. This kills the range. Most battery packs that are run down completely will start to show some aging after 100 cycles. We always suggest to people going as 'big' as possible, to start. People generally go farther as they get used to riding. That means they are using the last half of the battery. That means you are drawing from a 'smaller' battery, a 5 ah battery, because that is what is left. You won't get as much current, generally, especially toward the end of the battery.
I monitor what is drawn from the battery, with the Watts Up, and what goes in, with a Kill a Watt meter that goes in the AC plug. What you want is to see is a steady watt draw when the charger is plugged into the bike battery. It might be 100 watts or 150 watts, but it should stay there for a while. It might drop toward the end. But if you have a 48 volt system and you draw it down 8 ah, a 2 amp charger will need 4 hours, more or less, to recharge. You want to see that happening.
Most people are not going to get into the details, but it's fairly simple. It becomes a routine. You know what you draw out of the battery, so you know what you have to put back in. For me, I generally draw down about 8 amp hours, and I know my 2 amp charger will need 4 hours to recharge. I know where the final voltage will be, about 41.4 volts.
You should be able to figure out if you are 1) getting a consistent 8.5 amp hours out of the battery 2) whether the charger is putting that back (hours to charge will work) 3) what watts you draw as you ride, which means what speed.
4) whether there is a consistent voltage where the LVC is cutting out (low voltage cuttoff).
There does seem to be a drop in voltage when you start out on a fresh battery. Some of that is normal, and it could be a slight 'overcharge'.
Not sure what the battery chemistry is, or the exact nominal voltage. It would be different if you have a 48 volt versus a 52 volt, Lion or LiFePo. My LiFePo pack has a very tight range on the voltage, from 41.4 fully charged. That drops a volt immediately. It's rated 36 volts but that would be just about dead.