DC power question

Okay, so i have a 9 amp hr, 12v, lead acid battery that I am using to power a 12v dc fan. The fan uses 500 mA. In theory, and I know I'm new to this, I should be able to power the fan for roughly 9 hrs, reducing my charge 50%. When I run the battery through a potentiometer to recieve either 6v or 9v, is the fan still using 500 mA? I guess my question is, will my battery last longer? I'd like the fan to be less powerful and last longer.
Thanks

Some reading...

**broken link removed**

Thanks, Indulis.
I didn't know that Lithium rechargeable batteries also have recovery after a heavy discharge.
I salvaged some Lithium-ion cells from a few products and use them to power my RC electric airplane. It flies for about 20 minutes then the battery gets weak and the airplane cannot climb anymore but flies level when at max power. Then the motor speed controller senses that the battery is nearly discharged so it disconnects the motor and the airplane glides in for a landing. The battery is hot and the motor is very hot. When I let the battery cool (or recover) then it can power the airplane for another 10 minutes at full power. Then after another recovery it can power it for 5 minutes, then the next time for 2 minutes, then 1 minute, then seconds.

My IR controlled helicopters do the same thing.