Yes there is an iOS 6.1.5 update for the 4G iPod.
See:
Fixes an issue that causes FaceTime calls to fail for some users on iPod touch (4th generation)
See:
Fixes an issue that causes FaceTime calls to fail for some users on iPod touch (4th generation)
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Yes there is an iOS 6.1.5 update for the 4G iPod.