I have the exact same problem. Cleaning around the edges fixed the problem for about a week, then it came back with a vengence and cleaning again didn't help. I didn't even realize that tapping the trackpad could often substitute for clicking the button/bar, and figuring that out of course helped - but there are still times that one has to click.
I also discovered, however, that simply resting my plam or pressing on the topcase anywhere to the right of the trackpad activates the clickbar/trackpad button as if it had been pushed. It doesn't take much pressure either. This seemed to be the cause of some of my worst "stuck clickbar/button" episodes.
It's almost second nature to rest my right palm just to the side of the trackpad while using it - but being sure I'm NOT doing so has really reduced this problem. When it still seems stuck, sometimes just using a fingernail with a little pressure on the edge of the click bar/button closest to you and flicking upwards (like you're trying to move the button upwards) once or even a few times if necessary will unstick it.