Commercial metalworking stayed around all the time until today. It only increased and improved. (It's made of bronze, it's not like bronze working was lost.)

The tooling may evidence some kind of regression. I really don't know what kind of tooling was needed to create this, although gears by themselves and high precision in a single mechanism do not say much. From the looks of it, this devices requires a lot of theoretical knowledge, but not so much practical one (but that's an uninformed opinion, if you have information, it would be great). The theory was not lost in any way.

FWIW, the device is called an 'orrery'. When it was made in Syracuse, it wasn't a product of an industrial base, but was a project made by a certain sort of mathematician and scholar doing cutting edge engineering and applied mathematics. The Antikythera one seems to go back to the traditions from Archimedes' workshop which was amazingly advanced. Archimedes wrote a treatise on building them (now lost, alas). Orrery making in something like Archmedes' tradition continued on for hundreds of years outside Syracuse, esp. in Athens and Alexandria, and we have references to orrery making through the ages. The art of making them was a product of libraries and schools where they were created by scholars as an academic craft, not an industrial production facility.

It's not that industrial base.

If devices like the antikythera were commonly produced, we'd find more of them, and descriptions of them. This looks like a one-off achievement.

I'd rather say that this maybe more like a Saturn-5 of the day: a top achievement that required extraordinary efforts, and not very reproducible because of that. Most things around and in its production chain were not nearly as advanced.