It sounds to me like you have a wire edge. There are many here who can explain this way better than me, but I'll take a stab at it. (pardon the pun)
Anyway, when you sharpen a knife, once you "get to the edge" a burr will form on the side of the blade opposite of the one against the stone. You can feel it with your fingernail. It will sort of "catch" on the edge. You can sometimes see it if you have a magnifying glass and the right light. This burr forms on one side. It seems supersharp (especially on the side where the burr sticks out), will shave great, but the burr or wire edge is so fine that it will break off the second it hits something harder than a hair.
I think looking for that burr to form is key to doing a good job sharpening. Here's how I do it. I sharpen on a coarser stone on one side until I feel a burr form all the way down along the edge. I switch sides and sharpen until the burr is formed on the other side. I usually sharpen it back and forth, making the burr change sides each time. (it can be done with less strokes and pressure each successive time). I then switch to a finer stone (or from the corner of a sharpmaker stone to a flat). Do the same thing (making the burr form on one side, flip over, etc). Once you work your way down to the finest stone, then just keep alternating sides and reducing the pressure of your strokes until theres no longer a burr and it's sharp.
That's probably more of an answer than you asked for.
--Matt
