Should I refrigerate the artichoke bread leftovers?

I don't because it is usually devoured by the time I get home

Yes you can, and just heat it when you want to eat it.

Over the decades, I've never refrigerated.

You don't need to refrigerate it and it'll be good for several days

I would if it's warm out! If it take you a couple of days to eat!

It should still be good the next day as long as dont forget to consume it. Putting it in the fridge will probly harden the bread

If you'll consume the next day not necessarily.

Not necessarily