Q: Weird quirk

Firstly check if you have any other electronic devices, mice, telephone base stations etc in the vicinity.  They (it) may be causing interference.   You haven't said how long is the drain period.   Here are a few notes I have put together on batteries and expectations.

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Whether you use regular or rechargeable batteries you should buy the best. Discounted or unbranded batteries are more likely to give a depleted performance and may be of irregular size, often leading to connection problems.   Apple’s own brand, Eneloop and Energiser appear to be the best.

Rechargeable batteries for the standard Magic mouse are unlikely to exceed eighteen days before needing a recharge although the mouse itself can be a limiting factor.   I have seen reports that some Logitech mice vastly exceed this.    Apple may suggest more in their sales blurb but this is a realistic expectation.   The benefit (if you are organised) is that you can always have charged batteries available.   Regular batteries will give you between 25 and 35 days before they need to be replaced.

Note.  Never mix old and new batteries or rechargeable and regular.  

Both the above are based on my personal experience, not shutting down my machine and using it for around four hours per day.   Note.   Monitors do not always faithfully report battery strength, particularly with rechargeable ones.

When checking your mouse or keyboard batteries ...

Turn off the device.

Remove the batteries,

Clean the terminals both inside the battery compartment and on the batteries themselves.

Replace or renew both batteries.

Turn on the device.   You should get a blinking green light if the device is paired.

Click the mouse to activate it.  The green light becomes steady.

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