Unlisted 1868 Nickel Repun. Date, Lower Shield, Feathers, Arrows Doubled

Mintage of the coin that year was 28,817,000

What's the life of a die (remember, this a very hard alloy of copper-nickel)... couple hundred thousand? So how many dies were used during the striking process...

In 1868 for Shield nickels? About 15 - 20K. So you are talking about 1400 die pairs for that year, and possibly an even greater number of combinations. (This was why they were putting so many defective dies into production, and using them til they fell apart. The die shop could not keep up with the demand for dies. A toggle press striking Shield nickels would need its dies replaced a minimum of three times a day.)

And how do you know it isn't listed? What references did you check? There are a lot of known varieties that aren't in the common general references, and new ones are turning up all the time.

The doubling looks to be Machine Doubling which is common in this series. The RPD is pretty nice though. There are so many varieties for 1868 alone its difficult to figure out sometimes. Yours is a Reverse of 1868 with two broken letters (C and S) so that may narrow it down in your search.
Howard Spindel is the guru of Shield nickels, he may be able to help. He has something called the Shield nickel Viewer that is pretty comprehensive (more so than any other SN reference) His website is shieldnickels.net and there are links to the Shield nickel viewer should you want to learn a lot about Shield nickel varieties.

Doubling that is not on the date is Strike Doubling. The date doubling is an RPD 18 north.

It is not unlisted - it catalogs as S2-3006 in SNV.