I believe that styles die out over the years, generally because the head instructor/founder/ or whatever has passed on and there was.....
1) No one good enough or serious enough to take up the torch (so to speak) and carry the art forward.
2) The art or system was no longer needed and it died out due to lack of use.
3) The art or system didn't have a large enough following that gave it the momentum to survive long term after the founder's passing.
4) No clear line of succession so the art split apart and was renamed by all of the top students and over time it morphed into new arts.
5) Competition brought about by other arts coming in that were more popular.
Specific arts nowadays, names? Nope sorry. I can give examples of arts that died that I've read about.
In the book "Cebuano Eskrima Beyond the myth" in the 2nd half of the book the authors were doing just that, researching and documenting different styles or methods of the FMAs that were dying out due to the styles not be needed or no one to pass the teachings on to. These were mostly village arts or systems that were used to fight off Muslim raiders in days gone by.
https://www.amazon.com/Cebuano-Eskrima-Celestino-C-Macachor/dp/1425746217
In the book American Shaolin: Flying Kicks, Buddhist Monks, and the Ledgend of the Iron Crotch; the author describes meeting old masters in China who didn't have someone to train and pass the art on to.
https://www.amazon.com/American-Shaolin-Flying-Buddhist-Odyssey-ebook/dp/B000PDYVR0
In WWII many karate masters died in the war, along with their students and such and from that several styles and a lot of written texts on karate and Okinawan martial arts were lost.
Agreed. What we have nowadays is back door engineered some training methods from Europe's sword systems, American Bowie knife, European/American staff, tomahawk, American Indian systems etc. etc. but the transmission of the actual system wasn't really handed down unbroken. Passed down in tact from family to family or tribe to tribe.
A lot of research has gone on to try and replicate these systems but they weren't handed down like the Japanese/Chinese systems were.