I'd start by replacing the button. When installing I would make sure that it is well sealed from water intrusion, and doesn't look like it is made of plastic that will fail in a few years. Last time I replaced one I used a cheap brass non-lighted one, theory being that simpler is better, and the brown plastic button might be more durable than a plastic that also had to be translucent. Was I right? Who knows...

If you still have issues with the bell not working reliably after that, then think about replacing the indoor unit. Or if you jjust don't like it, this is a good excuse to do so