Have you switched off the Meike grip when you store it away? Make the white dots out of alignment on the switch mounted around the shutter release button.
Silly question, do you switch off your D7000 using the main on/off switch on D7000 body?
I always keep AA cells in the grip all the time and no battery in D7000 body. It lasts a long time, days... I don't know if it will store for more than a week because I use my camera too hard, around 1000 shots within days.
Also, I normally will switch off the grip too, but there are many times I forgot. There will be some opportunities to test this power drain issue when I restrain myself from using the camera with grip attached for a long period of time.