A recent test with fresh AAA batteries and the micro:bit displaying a single LED always on lasted 6.5 days.
If you use the batttery pack with the micro:bit and want to prolong battery life further there are some tips you can follow:
1 - Disconnnect the battery pack after use and if you are not going to use it again for a while, remove the batteries
2 - The radio function once on is always listening for signals, so this can drain the battery. Disconnect the battery pack when you are not using it
3 - If you are driving third party accessories or peripherals such as LEDs, these will also contribute to battery drain, so you may wish to use a seperate power supply to drive these.
If you have any more tips, get in touch