Mine tend to last between 6 and 12 weeks. Duracell Ultra or another decent quality high capacity type make the best sense. You can get much cheaper AAAs, but you end up buying more of them to the point they cost more long term. The VIP remote is quite demanding, and once the batteries' voltage drops too low (once they've lost most of their capacity/charge) they'll not operate the VIP any more. They will however have enough charge to run more normal devices, like infrared remote controls. I keep the ones my VIP uses up and put them in other devices rather than throw them away. I'm not sure how well rechargeable AAAs would work, as they start off at 1.2V, but if they stay there and steady for long enough, it might be worth a try if you have any you could use temporarily from another device in the house.
One thing to try is flipping the remote control upside down if you're not going to use it for a few minutes. Doing so disables the Air Mouse function, meaning the internal accelerometer (or is it a digital gyro?) isn't draining the batteries at all.