One thing to check: Apple menu > System Preferences > Energy Saver > Battery > Put Hard Disks to Sleep when possible.
Other than that, I'm not sure. This isn't an area where I have any expertise and little personal experience. One possibility is that various drives may have different features and may have different sleep settings. I would try it a couple of nights with the drive disconnected and a couple with it connected and see what the difference in the battery is.
I rarely shut down my MacBook Air -- maybe once a month on average. I usually charge it in the evening, disconnect the power, close the lid and it will be at the same percentage in the morning as it is the night before.
Also, while the battery isn't removable by the user, it can be replaced for $129. My Air is 3 years old and the battery is still in good shape.