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, or if you are programming using micropython use radio.off() in your program.
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