I got an Ibanez AEL40SE with a B-Band® UST™ Pickup. When recording, notes on the highest three frets seem to fall out. I uploaded a small sample to my profile. Does anyone know why this might happen? Is the pickup broken?

If its the "untitled" sample then there is nothing wrong with your pickup - you need to adjust the action.
it's very hard to "break" a pickup. It's just a magnet, slugs, pole pieces and wire.
If a pickup is broken, it will stop producing sound. It won't selectively drop three notes.
You need to adjust the action and possibly level the frets.
action is too low
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Ok thanks, I'll look into the action. Strange though, the strings sound just fine to me when I play the guitar acoustically.

Raise the pickup?
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xjosheex, you have made a simple answer to it all haha

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Raise the pickup?
Okay....how exactly would you go about raising an undersaddle piezo transducer, eh?

Try everything above. Then put on some heavier strings and make sure you've got a nice fresh battery in that preamp.