I tried to take a close look at the radius, by comparing it to the radius of a Zeppelins cloak and a Zeppelin's Range increase. From as close to a top-down view as I could get it, I placed a zeppelin as close to a mine as I could, and scattered units in a radius beneath it. I activated cloak and looked at what units under the mines radius were cloaked.

Aerial mines seem to have a trigger radius of about 500 m. Imp Fighters have a maximum firing range of 875 m, and can fire while moving.

I will TRY using Aerial mines in actual combat situations, but it seems to me that if the balloons drop the mines and run away, the imp fighter(s) can probably shoot the mines down harmlesly, and then go after the balloons, whose mine skill will still be on cooldown.