It might be worth having someone up there to fix the equipment when something goes wrong... unless by that time we've developed teleoperated robots with the flexibility and dexterity and sensitivity needed to make arbitrary on-site repairs. You might remember from the Hubble repair missions [1] that these relatively simple tasks you might expect to take a few hours in an Earth-based lab took /days/ of EVA time. Imagine how much more difficult such things would be when you have to squint at the job through a camera (not as good as an eyeball), use clumsy manipulators instead of your fingers (you'll have force-feedback if you're lucky, but forget about feeling textures), and with some lightspeed delay on top of that. Don't underestimate the value of other human senses, either; often the first indication of a machine failing is that it sounds or smells wrong.
I suspect this would be the likely case, and there would be repairs / refueling / retooling. If asteroid mining was anything like planet mining the ability to adapt tools on the spot and evolve quickly was a huge boon.
One of the places I like to camp is Plumas-Eureka State Park [1] which is the site of an old gold mine. The stamping mill is kind of still there. One of the things the blacksmith docent talked about was that there was a competitive advantage at a mine to having a creative blacksmith, since they could build tools well suited to the kinds of rock and conditions rather than relying on 'off the shelf' sort of designs.
[1] https://en.wikipedia.org/wiki/STS-125#Extra-vehicular_activi...