Using a H-bridge, I've connected my DC Motors to an Arduino. When I accept the external power source from a wall, using a 9V battery eliminator, the motors spin well and consistently. However, when I connect it to a 9V battery, the motors spin slower, and the speed deteriorates till the motors stop. This happens in approximately 5 minutes. I checked with multiple 9V batteries of the same type. I have tested the batteries to check if they're dead after the motors stop. They are not, and if I reconnect the motors to them, the same process occurs all over again. I have checked for short circuits, and there are none. Any possible ideas as to why this is happening?
First off, never use 9V batteries to power motors or any device that consumes more than a few hundreds mA. Those batteries are just too weak.
Now a battery eliminator is not a pure equivalent as it can typically supply 800 mA or more, depending on the model you get.
The only commonalities between the battery and the eliminator are the 9V voltage and the socket.
If you want to power DC motors with batteries then rather use several 1.5V batteries in series.
The question is not about volts, but current.
A 9V battery is notoriously bad at powering anything that requires high current, like running a motor. Due to to chemical nature of the battery, the 9V will struggle to keep supplying enough current and will fairly quickly drain.
A regular alkaline 9V block can supply you with 565 mAh, which is not much if you power motors. You'll have more luck with LiPo (lithium polymer) batteries, which are capable of supplying 2200 mAh or more!
To learn more about different types of batteries check out https://learn.sparkfun.com/tutorials/battery-technologies
Wall power can quite easily provide the required current your motors need.
Batteries use a chemical process to produce power. If you draw to much current (motors use quite lot) the chemical process can't keep up and the voltage will drop, resulting in a slower running motor. Try connecting two batteries in parallel. That way each battery only has to produce half the current.