Southwest Regional Forester Calvin Joyner outlined his decision in a letter last week.
Craig Thiessen had appealed after the permit was revoked in November, saying he had no livelihood without his cattle grazing in Gila National Forest.
Thiessen pleaded guilty last year to knowingly taking threatened wildlife. The 10-month-old wolf pup was fatally struck by a shovel in February 2015.
Fish and Wildlife Service officials said the wolf died of injuries Thiessen inflicted.
Thiessen stopped short of admitting to killing the wolf in his plea agreement.
There are about 130 Mexican wolves in the wild in New Mexico and Arizona.