If one starts building new parts from scratch there may come a moment where people say something has become a replica, more so if one also uses new technology (philosophers discuss this as https://en.m.wikipedia.org/wiki/Ship_of_Theseus).
The weird thing, though, is that the road along which one gets to an object is more important than the end result in determining authenticity. Replace all parts of a spitfire until just one piece remains original, and you have an original spitfire. Build a replica, buy that one original part, and include it, and you still have a replica.
A nice example is HMS Victory, a wooden warship that saw battle at Trafalgar. It is kept afloat by replacing its parts. By now around 20% of the original wood remains (http://edition.cnn.com/2011/12/05/world/europe/hms-victory/). Yet, we think of it as the original ship.
However, it is not a given that replacing all parts makes a new object. The Ise grand shrine in Japan is over 2000 years old, but gets rebuilt with new materials every 20 years (https://en.m.wikipedia.org/wiki/Ise_Grand_Shrine)
My personal opinion is that wrecks dredged up from swamps and such should be put into museums as is. Flying airplanes should be replicas, made as close to the original specifications as the owner wants.
For example, a few years ago there was a project at Paine Field to build flying replicas of the Me262. They took apart an original to measure everything and make a specification. As a concession to safety, they used modern jet engines and instrumentation, and used lead weights instead of guns (to maintain proper balance).
I would have bought one if I could afford one!
Nobody would actually want to fly an original, because the engines only lasted about 20 hours, were extremely unreliable, and nobody bothered with corrosion protection (didn't expect the machine to last long enough to corrode).