Logitech M705 Wireless Mouse: Are the batteries dying, or does the device have a hardware failure

I have a Logitech M705 wireless mouse. I'm first time using a wireless mouse, so I don't have much experience with the hardware features and behavior.

It is rated that it runs for 3 years with the same batteries. I think this "3 year" rating is calculated for a very low usage and activity; like 2 hours a day. I'm using it for about 12 hours a
day, so I expect it to run out of batteries in a much shorter time in my case.
I have been using it for about half a year. Recently (for the last two weeks), it started to make some peculiar behavior when clicking and drafging objects.
– When I click something, it sometimes double click it.
– When I drag something from one place to another (or selecting some text), it sometimes drops the object in the halfway (when selecting text, the text which had selected up to that time becomes unselected and it starts to select the rest of the text from that moment), but it goes on being in the "left-button-pressed" state. It is like, the pressed button switches to "unpressed" state for a moment, then returns back to the "pressed" state.
When one of these faults occur, it occurs several times sequentially.

There is no problem in pointer movement, scrolling or right-clicking.

Since the batteries last for a very long time for this device, I don't expect it to stop working in an instance. I expect it to give these kind of syndromes of a time period.

My question is;
Is this how batteries run out for a wireless mouse?
Or, is this another kind of hardware/software problem?