By the 100th visit they'd get suspicious that you're scoping out the joint for a terrorist act.
So, same question, and this time really think about it: you are capable of keeping an eye on a limited number of potential threats, you can never completely disprove that any individual means you harm, but you have to look as carefully as you can at the most plausible threats in the time you have available. How suspicious is my behavior, and what evidence would it take to convince you that my threat is negligible? What about the idea that you might personally be blamed if you cleared me and I later turned out to be a terrorist: does that affect your calculations? If so, is that in the best interests of the airport, or just you personally?
That assumes that on-scene guards ask questions of the subject before reporting observed suspicious behavior (which may or may not be the case, and is even less likely the case in the event that the "guards" that observe the behavior are automated face/gait/etc. recognition systems looking for unusual patterns.)