why is the united states is the only remaining postmodern nation that retains the death penalty?

Good question!!

Are we a more violent nation?

Haven't we outgrown our frontier-justice mentality?

Since many claim we are a Christian nation, are Christians more punitive than other religions?

You may get some ideas from these articles.

http://www.deathpenaltyinfo.org/node/2408

http://en.wikipedia.org/wiki/Use_of_capital_punishment_by_nation

http://en.wikipedia.org/wiki/Capital_punishment