The biggest influence we have is the massive influx of money due to oil sales and military assistance.
As long as we remain unwilling to pay more for other energy sources--and I think that is coming, as concern about global climate change and rising oil prices combine to change the calculation--we can't really ignore the Middle East. (And we won't stop giving the second, because that is a tool to help insure the oil supply.)
So my perspective is that we've been involved all the way along--but often in unproductive ways from the standpoint of social progress, and hence a stable peace, in Middle Eastern nations.
Analyst Thomas Friedman has put it that we've treated the Arab nations as a "big, dumb filling station."