There are two chips in a MagicBand. One is for long range functions and uses a battery, the other is for short range functions and works passively without battery power.
Long story short: A MagicBand will work pretty much indefinitely for park entry, FastPass+, and most things that require touching Mickey to a reader. But the stuff like automatic collection of ride photos/videos and the "magic effects" on certain rides requires the battery, and it dies after a while. How long? That's hard to tell without actually using it and seeing if it works.