Quite often after many boolean operations, objects become broken, in that they don't accept further boolean operations. (Sometimes objects also become "joined surfaces" instead of "solids", but that might have different causes.)

Usually at that point I just rebuild them from scratch. It's usually not too much work because I can use the broken object to snap to, but I'm wondering if maybe there is a faster way to repair such an object?

Like the one in the attached file. I was trying to cut out (boolean diff) the rectangle, but the object is done, it doesn't take any more boolean operations. Time for a rebuild I guess.