I just refinished a dresser with a tinted poly finish to roughly match the other wood tones in its new room. I didn't do the greatest job in many aspects - it was my first experience with poly and I don't really have the patience required for mirror-like finish work on furniture - but the end result is passable.
One of the things that kept me pulling my hair out was the ease with which the finish came off at the corners when smoothing between coats (I was brushing it on instead of spraying, and so I was also forever smoothing out brush strokes between coats). It didn't matter if I was using the ROS or hand-sanding, what grit or material I was using (I usually started with a light pass of 320 grit with the power sander, followed by detail work with 4-0 steel wool by hand and a finish pass with a Scotch-Brite style pad on the ROS), or how many coats had been applied (lost count; the goal was to get dark to match the espresso/black cherry finishes of other pieces, so the piece got at least three full coats plus touch-ups), all it took was one pass too many, too close to an edge or corner of a panel, and a line of bright bare wood shone through the dark red-mahogany finish, forcing me to apply more touch-ups and then sand the brush marks smooth again, potentially undoing the touch-up or uncovering another edge elsewhere.
Given the total time the project took to look halfway presentable, I could have sanded the whole thing down to raw wood, stained it nice and deep, then finished in three or four coats of clear poly; this product was supposed to be easier than all that to change the tone of an already-finished piece, but nothing doing. That was probably mistake number one; going for a quick fix over doing the job "right". However, even doing that with my sanding technique (or lack thereof) would have left the corners unfinished, the only difference being that it would be harder to tell if a corner was still raw, as the stain will still show fairly dark, but there'd be no poly protecting the wood.
I understand the physics; the pressure of the sanding media on an edge or corner, in pounds per square inch terms, is infinitely more than when sanding a flat surface as the edge ideally has zero surface area. That means it's much easier to burn right through any layers of finish you've managed to build up over that edge.
The question is, how to overcome the physics and preserve your corners, without just rounding them off? It can't be as simple as "don't power-sand your finishes" as even when I worked by hand it was ridiculously easy to remove finish along the edges (easier, in fact, as with hand-sanding the paper or pad wraps around corners more easily).