The only time the RPM will go down is when the transmission changes gears (if an automatic) or when you let off the gas. When you step on the gas, the RPMs go up, that is what it is supposed to do. If the car is not changing gears then you need to get your transmission looked at.
Do you understand what you are saying? You said "when you accelerate the rpms won't kick down until you let off the gas." Duh! That is precisely when the rpms should go down. When you let off the gas!
