Im not really sure. It is very hard to describe, and of course very subjective. Everyone has a different idea of sharp, therefore everyone is going to have a different idea of dull. I don't sharpen nearly as much as it sounds like some pros here do. I usually sharpen once a week, rotating through out that week between about 3 knives, but my knives would probably still be called sharp by my coworkers. I usually do not feel the need to strop or touch up the edge on my Mac black ceramic hone.
I like cutting paper while sharpening. It helps me find dull sections or remaining burrs. So I would say I would consider a knife dull when I could not cut paper after trying to bring the edge back with strops or a ceramic rod. If I can't do that, then it is time to go back to the stones.
"God sends meat and the devil sends cooks." - Thomas Deloney
I dont think anyone in a real pro setting is pulling out a tomato or a piece of paper to test their knifes sharpness. Isn't it just a feeling? When I use a knife on the protein station on a weekend night (going in perfectly sharp), after slicing proteins including grilled hanger steaks, blackened duck breasts, coffee crusted pork tenderloin and pan seared airline chicken breasts, all night I can "feel" the meat pull and tear a little. As soon as I have time, I'll strop on mid grit stone to refresh a toothy edge. As far as blades used to do vegetable prep (tomatoes, etc...), I use a much more refined edge and will strop on diamond loaded leather frequently.
I break out the stones every Monday, (not always for the same knives, and often for others knives as well).
With certain knives what CaddyJ said is right on. My Masamoto, Takeda and Kono HD will keep an "adequate" edge much longer than say, my CCK cleaver or certain stainlesses, which starts sharp and just gets dull fast.
I think once you experience a good quality knife with a perfectly keen edge, you have expectations, and are no longer happy with "adequate'.
The difference between try and triumph is a little "umph"! NO EXCUSES!!!!!!!
The psychological effect of marginal/relative sensitivity also is at play here! If you take a hair splitting edge and it tapers down to a paper cutting push cut edge, it will feel as if it has dulled more than a coarsely sharpened, toothy Wusthof that is relatively close to a dull (by most of our standards) edge: think of a knife that is sharpened to a 2 going to a 1 vs a knife sharpened to a 9 going to a 5.
Given this, when my knives fail to do the task they are intended to do in a manner that is comfortable for me I think it no longer retains its edge. For example if my Western Deba fails to cleanly split a stack of white corn tortillas with minimal downward force, or begins to tear through bacon instead of slicing it, then I will take it to the stones. If my Honesuki no longer glides through the chicken along the ribcage and exhibits tears, I feel its edge is no longer retained, and thus it is time to resharpen. Like most things in life, I find that its good to use common sense and judge case by case, avoiding a universal rule!