I'm 50 and this conflict has literally been going on longer than I've been alive.  There have been ebbs and flows, ground gained and lost, population shifts, but no new progress.  I've come to the conclusion nothing will change unless we change the parts of the equation drastically.  I take a 30,000-foot look at this, and most, problems of the world and I believe in turning problems into solutions and in synergy.  Keeping that in mind, here is what I see and propose:

The Palestinian people are now de facto split into two regions.  For simplicity, let's take the most violent region - Gaza - for now.  The basic problem, beneath all the rhetoric and mutual blame is this:
The militants launch missiles, almost daily, and then Israel, understandably alarmed, retaliates with superior force.  Geographically, Israel controls access to Gaza from the sea, north, and east, but not south, which is where a lucrative tunneling business keeps the Gaza militants supplied with weapons to fire on Israel.  Egypt intervenes only lightly, if pressed, and mostly not at all, because their own population would not stand for them blocking the "tunnel trade" to protect their cold enemy, Israel.
OK, here's how you turn a problem into a solution, though I admit all parties would howl at first suggestion of this.
America should broker a deal to redraw Israel's southern border 50 miles south of Gaza, relocating Egyptian villagers away from there, with money and rebuilding support and in coordination with Egypt.
The benefit for Egypt: Egypt gets this mess off their back door.  They can still be pro-Palestine, and anti-Israel, but with only a border with Israel, their peace treaty with that country would apply.  They would not have to worry about tunnelers; that would be Israel's new problem.  The Muslim Brotherhood etc. would protest, but in the end, they will neither attack Israel, nor do anything more to destabilize Egypt than they are already doing, and if humanitarian aid is provided by the United States (see below), that should mitigate some of this protest.
The benefit for Israel: Control over the access points where weapons are smuggled and eventual reduction in violence through de facto reduction in the factors that cause it (missile parts and guns).  Also, perhaps, a chance to move settlers to these new lands and off the West Bank, so that the West Bank might truly become a Palestinian state someday.
The benefit for Gaza Palestinians: Not obvious at first, but there can never be peace if the militants are allowed to fire into Israel indefinitely.  This "lifestyle"- choice has to end so that a true building up of the bankrupt Gaza economy and an end to the blockade can begin.  America, as well as Israel, can help with this, but the shooting has to stop first.  This is a war and it has to end before peace can begin.
The benefit for the United States: Taking control of the situation in a novel way that brings peace to both sides would be an immeasurable coup for America, worth almost any price.  It would end the "cause,"- manipulated by Iran and Syria for their own ends.  It would provide a true way forward, and repudiate the poorly drawn and forever controversial British lines in the sand.

I'm too old to have much hope that the current dance will ever accomplish anything, except maybe by accident, or worse, by horrific miscalculation costing thousands or millions of lives.