This is NOT problem with your mouse and its batteries. This is Apple NOT supporting older hardware correctly. HS is not reading the battery power right and it shows incorrect % in indicator. I submitted bug report to Apple months ago on this. They send me eventually back e-mail, that they are closing the bug report as "Yes, we can reproduce this. But NO, we are not fixing it as these mice are obsolete devices. Buy new mouse with rechargeable built in battery. There it works right."
Yes, that is correct summary of their e-mail.
I have like 6 of these old mice and they seem to last longer than the original Macs themselves. I am not replacing them!
If you simply ignore the % battery value, you will find out, that it drops to something like 10% and then it lasts for long time. In reality, you will get about same life from the battery as in prior versions of OSX. I have learned to ignore the battery value.