By coincidence, I'm wearing an Accutron 218 today. As others have posted, they are tricky to work on with some extremely delicate and sensitive parts. You do need someone with expertise, but to them I think it would be a routine job.
I bought this watch (and another similar) from an ebay vendor in Bulgaria "anticvarius". I do not know if he also services them for third parties, but he generally has a selection for sale, and he seems to have done a good job on both of the ones he sold me including re-phasing them to work with modern batteries - the original mercury batteries have long since been banned and had different characteristics.
The only other option I know of, is in the UK -
http://electric-watches.co.uk/service-and-repair/
They may be an historical oddity, but work extremely well, and I think worth keeping going.
Edit - I think citizen won't want to know - they produce Bulova watches called "accutrons" but it's only the name they have (mis?)used.