As far as I know, there is no living lineage in
pure rapier fencing. However, classical fencing has quite a long lineage going back to the 1700's. For example, see the lineage of Maestro Sean Hayes:
http://www.northwestacademyofarms.com/aboutteacher.htm
Note the first master noted was possibly actually around when the rapier was still in use, since it saw its decline in the 1700's. The lineage is that classical fencing retains much of rapier technique minus the grappling. A good grounding in Classical foil and epee will give you an excellent start for solid rapier fencing. Also note that in Spain, the smallsword never really entirely replaced the rapier... they just made smaller rapiers.
What I think classical fencing guys tend to think is not that there is a lineage of rapier
per se, but that much rapier technique is
preserved within classical foil and epee, which is probably correct. If I were a rapier fencer (I just dabble), I would certainly seek out instruction in classical fencing, since that's as close to a living rapier lineage as you're going to get.
Keep in mind I'm not a fencing historian. If you want the real goods on this, I would recommend contacting Maestro Hayes directly and ask him what he thinks. He's never claimed to be more than what he is, and from what I've read of his posts on various online fora, I'm very inclined to think he's a straight shooter.
Best regards,
-Mark