Unfortunately I don’t know about the battery life…Fortunately these take either CR123A batteries or you can use the micro USB port in the battery compartment. It’s not ideal, but maybe running a long micro usb cable might be a good option. The mount is also magnetic, so it’s easily removed to change batteries if you need to go that direction.
I read in another forum/thread that using rechargeable CR123A batteries messes with the motion sensor, giving false motion alerts due to battery voltage problems. I just decided to go with keeping it powered via USB to get around all the battery issues. You also cannot use batteries and the USB at the same time. The USB port straddles both battery slots, so I don’t see how you could fit even one battery and use the port. The documentation does say you can operate using one battery or two.
The issue with keeping it USB powered is the battery door doesn’t close with it plugged in. To account for this, I just drilled a small hole to let the cord pass through. You can also just leave the battery door off or there may be some extra slim usb cables that might fit with the door closed. Besides these small issues, it works just fine with USB power. (fwiw: The sensor is still an end device and doesn’t route when plugged in)
I feel like such a huge fanboy for these sensors. I have 4 of them and I love how responsive they are. They’re on par/better than Philips Hue motion sensors in my setup and I love that they’re significantly cheaper and never need batteries. I highly recommend these even with the reporting weirdness.