Hello, just to clarify - by "run" you are probably referring to the edible ink smudging or "bleeding".
Edible ink (or any ink for that matter), will run or smudge, if it is not allowed to dry properly, or if it is printed to a substrate that it is not intended for. For example, edible ink is water based, so will not mix well with oily substrates. If you printed to an oily substrate therefore, the ink will ultimately move thereby creating a "run" or "smudge" or "bleed", technically, because it is not well adhered to the substrate to which it is printed to. But if you print to non oily substrates (such as fondant, and many more substrates), it will not run, and is pretty stable under average temperature conditions. Of course if you subject it to high heat, it will melt (and thereby, run). So the short answer is, under the proper use, it will stand up pretty well, and you can see many examples of pictures that InkEdibles customers and users have posted on instagram.com/inkedibles