Are you sure that the trees are not the problem? If grass starts out well (before the trees fully leaf out), and then slowly dies as the season progresses it could be a lack of sun, and/or water saturation after rain. It doesn't take much of the variables listed above to kill grass regardless of what the seed companies say(full shade, shade tolerant, etc).
It comes to a point where you might have to cut your losses and just create a mulched area around your trees with decorative shade perennials. Variegated hostas and ferns are shade tolerant and very hardy.
Don't give up the fight, just temper expectations and it will look awesome.