Just because you received a letter from a law firm doesn't mean they are going to proceed with it. This is just the beginning of a dialogue.

I, however, advice you to speak with a local attorney and get his consultation regarding your case. I'd rather spend a few hundred dollars but make sure my work doesn't go down the drain after years of effort.

I am trying to find an article that I read a few years back that suggests that copyright liability ends in certain number of years. In other words, if you are a holder of the copyright and someone else has been using it for over 5 years (hypothetical number), you cannot seek damages.

The problem here is a bit strange. They seem not to have a trademark on the name, so they are going after a "copyright"? What copyright exactly, if you are not even in the same industry? The domain consists of all dictionary names, they don't own the names, so I think they are just trying to muscle their way through.