I'm 54 and ride a fixie, with drop bars. Tell 'em that at your LBS. That should really mess with their heads.
My own LBS is Harris Cyclery. Nothing seems to phase them much. If an 80 year old were to come in and wanted a broken spoke replaced on his fixie, it wouldn't phase them.
If someone came in with a nice old 3-speed Raleigh that they had purchased at a yard sale, and they wanted it totally overhauled, they'd do it. They have a large inventory of parts for those. That customer would never hear excuses such as "Oh, no one uses those anymore". Sorry, I digress...
Heck, one of the co-owners of Belmont Wheelworks is John Allis. The gentleman is in his late 60s (I think) and I believe he rides bikes with drop bars all the time.
I think it all depends on the LBS in question.