I find rechargables only last a few days in mine, alkaline last 3 or 4 months
Try some Sanyo Eneloop XXs - high capacity and very low self discharge. Well worth the extra cost.
I don't think the brand would matter in this case, I think the nominal voltage is too low for such a low power device.
http://eznec.com/Amateur/1.5_vs_1.2_Volt_Batteries.pdf
Soz, the article is 'dangle berries'. Well technically correct, but 'dangle berries' for real life.
If you were designing anything that needed a constant drain of 0.5A or 1A, you wouldn't design it to use AA cells.
NiCd and NiMH batteries do outperform std alkaline batteries in high current applications, but are generally NFG in low power applications designed for alkaline batteries.
In this specific case, I have tried both NiCd and NiMH in the mouse, and got feed up with the contsant recharging required.
The Sanyo XXs last 2 months in my bluetooth mouse. Normal NiMH don't and NiCads I wouldn't bother trying (assuming you can still get them easily). I think the key is the low self discharge rate of the XXs. Low discharge NiMHs like Sanyo's Eneloop and Uniross's Hybrio now enable use in low drain devices.