I'd like to hear from other R09HR owners about what happens when the power runs out. It will be useful to know if the R09HR routinely loses the file or corrupts the file a the point when the battery quits. Or maybe the R-09HR can't tell the power left in a rechargeable AA as well as it can an alkaline AA?
I am not sure how the R-09HR does it, but electronics are not as smart to guess what battery type you are using. They read voltage and current, and respond to that. In fact you have to be careful in choosing rechargeable batteries and seeing when it reaches 1v/cell, or the battery may be damaged.
The reason why alkalines last longer is because they are 1.5v and rechargeables are 1.2v. I am not sure what is the amperage of an AA alkaline, but rechargeables are 2700mA at most. You can guess what consumption your unit has by timing how long a 2700mA rechargeable will last. If it lasts 8 hours, then it drains approximately 337.5mA.
When the batteries are used inside the unit is fine, and it's unlikely the battery will be damaged. But be careful if you use external battery supplies, as they have a lower voltage limit which shouldn't be exceeded.