Obviously, having replaced the battery for a new one and ruling out the possibility of having one that is self draining, the cause of drain is therefore likely to be in the Vehicle itself.
As suggested, the most common cause of this is the BeCM not going to sleep as it should for some reason. This results in it constanly drawing one or two Amps rather than a few milliamps. And that sure fits your time frame. The BeCM constantly monitors about 20 inputs, any one of which will cause it to wake up or stay awake.
Also as suggested, the most common cause for the BeCM not going to sleep as it should is due to the RF receiver constantly telling the BeCM that it is receiving a transmission in the frequency range that the Fob transmits and that it must validate in the event it is the owner with a valid key fob transmitting the right code and wanting to unlock the vehicle.
The problem being that some early RF receivers had such a wide band width of acceptable frequencies that even the close proximity of a set of automated supermarket doors would appear as possibly valid Fob transmissions, and close proximity to a transmitter of any kind can quite easily upset the BeCM and constantly keep it awake, thus draining your battery as indicated.
Later versions of the reciever accept transmissions only on a much narrower band width and unplugging the reciever can prove this is your problem, But as Rick states, in light of this, updating the receiver realy is a must anyway.
However, these are only what is commonly known, and there are other possible reasons that your BeCM is staying awake you must not dismiss.
A faulty door ajar or lock switch can do the same.
How to do a BeCM sleep test is detailed at the bottom of our systems help page, located here
https://www.blackbox-solutions.com/shop/help/SM022.html
I hope this helps
