Omega will take a watch from any era in for servicing, so they don't have an automatic cut-off date in terms of how old the watch can be. They may not have the parts to service it, but that doesn't mean they won't at least look at the watch to see what's needed.
Omega policy requires that parts are available for any given model for a minimum of 20 years after that model is discontinued and the last watch is sold from the factory.
There are really 2 categories of spare parts in question though - movement parts and case parts. Movement parts tend to be available for a very long time, so if you consider that they haven't made a 55X or 56X movement in 40+ years and all the spare parts are still available, I think that speaks to their level of commitment to keeping watches ticking.
Case parts are a different story, and in general they tend to be discontinued far sooner than movement parts are (they are still subject to the 20 year rule though). This often results in the specific part that is available not being exactly like the original, because Omega policy allows substitution to keep supplying parts for watches. So the crystal, crown, pushers, hands, dial, etc. may be different from the original if they are replaced.
Cheers, Al
