I would suspect the doorbell button. The front door button normally would get the most use and would be the one most likely to fail.

could be moisture/rust/corrosion in the Button or circuitry

When the battery goes low it can cause odd behavior. OR if the
battery has leaked it could cause connections to occur.

Taking apart the best you can and brusing out any kind of
corrosion will help. Check the batteries closely for any
kind of corrosion. Do it carefully so you can see any
small amount of white powder. If there is then track down
where it might be and do your best to dust it out, blow it
out. Don't blow with mouth. Spit will put water into the
circuit. A vacuum backwards is OK. A dry brush is probably
good enough.

Do you have a photo? What's the brand and model? IF I look
at it maybe it will help me get an idea.

IF the button has been pushed too much then it might be
squashed and 'always' on .. you'll have to devise a way to
pull it out so that it is 'out' and only in when it's pushed.

By photos I might help. But that problem will have to be
dtermined first. Can you make it beep , for sure, by
pushing it? Do you push it as hard as before or barely?

Thos kinds of investigations will be how you'll figure out
where the problem lies. It's a mechanical thing or a
damage from leaking battery thing .

Does it sit outside in moisture like FOG? Then it could be a
moisture thing.

And I Can help but there's a lot I can't do from here.
You'll have to send along or include more information which
you've thought through to determine if maybe there's some
causes for its failure.

IT should be 'fun' anot hard work.

Enjoy it. I'll be here and help.

Andre

I had a similar mystery with an older hardwired doorbell. It turned out to be friends of neighborhood kids sneaking up and depressing the button.