Ballistic Enchantment Buff is affected by debuff reduction and cleanse.

[tvgritz]

The Ballistic Enchantment buff gets cleansed by Dispel Magic, T3 Jumpstart, and T3 Cube. The duration is reduced by debuff resist, and if you are immune to debuffs (such as during Ivy's Stoneform) you do not receive the buff.

 

[BeyondLucky]

Youre right it does, I just tested this.

Debuff Reducer makes the buff last only 10s instead of 14s and it does not reflect that in the item tooltip at all. Not to mention dispel magic completely removes it.