Maya will (frustrating) for some reason delete one vert out of the four on any quad if you select them all...I dont know why but it does. If you do this on any part of your model it will always delte the 'corner'...must be the way it interpolates the grid/mesh. As dave has pointed out...clean mesh....OR if its the way Im reading this...merge verts...if you set your merge proximity to certain levels you can achieve it as well (if Im reading this right?). I personally hate using the clean tool as it will not do what you want and create LOTS of edges...etc etc etc when you do it...even with manipulating the tool options...its almost a boolean kind of thing and you have to manually do the cleanup after the cleanup LOL. I think you can (Jay/dave) physically identify the verts/faces and clean them only...not sure. I know you can keep hard/border edges in the clean tool...dont know if this will help you at all. At best personally (if there arent tpo many)...select the corner verts first...then shift select..and this will highlight all of the verts you want...then merge....or delete....

cheers bullet