I have new batteries (2 12 vold 20AH) and new tires (4.10/3.00-4) and the scooter only runs for about 25% of the time it used to before the batteries require recharging. Could the motor be dragging and requireing more power than it used to?
That could be caused by some sort of drag in the wheels or brakes. To check for drag turn the scooter off and prop it up on a stool or toolbox, then rotate the wheels by hand to detect drag. The front wheel should spin freely for a while after giving it a good spin. The back wheel may not spin freely though because of the natural drag that the motor creates, but it should be fairly easy to turn by hand. If you remove the chain or belt from the rear wheel then it should spin freely for a while after giving it a good spin, if it does not then the rear brake may be dragging and need adjustment.
Another thing to consider is that new batteries need formatting for 20-50 cycles before they reach their full capacity. Here is a chart showing the life cycle of lead acid electric scooter and bike batteries including their formatting, peak, and decline life cycle stages.
So, I should deplete the batteries and recharge them at least 20 times?
Yes, I recommend depleting the battery pack by using the scooter, that way you will get the maximum use from the battery pack. Each time the battery pack is discharged and recharged you should notice increased capacity.