The Arab-Israeli conflict has persisted since 1948, because, frankly, the Palestinians and many of the Arabian states fail to either accept or they break the treaties created by outside influences to help the situation in the area. The only two countries that have signed treaties with Israel is Egypt in 1979, and Jordan in 1994, with Egypt being the only country that really holds to their treaty.
Why would the Palestinians and Arabs continue to persist in their want of destruction for the Isreali country? After all, the Palestinian Covenant, formerly known as the Hamas Covenant, the ruling party and a terrorist organization, demands that they would not stop attacking Israel until it is utterly destroyed. When this is indoctrinated into the people, they fail to see their neighbor of Israel as human (see where this is going? World War II?), and continue their aggression in an effort to "take back their homeland", in which it wasn't even rightfully theirs, and to exterminate the Jews (which sounds a lot like the Nazi Doctrine during World War II). With this in mind, most of the countries and terrorist organizations would accept nothing less then the removal of the state of Israel, and the destruction of her people.
On top of that, there are many groups in the US who fails to see the conflict in it's light of truth. For example, the LGBTQ+++ community heavily condemns Israel (ironically), even though Israel is the only country in the Middle East to allow the LGBTQ+++ community to have a presence. Other countries, particularly European ones, also fail to see the benefits of having Israel in the Middle East as a safe haven for military actions in the area, and focus on feeding the Palestinians "tablespoons of power" by condemning Israel in U.N. meetings, much to no effect.
How should one go about to regaining peace in the area? Ironically, the way to maintain a fairly <em>uneasy</em> peace is to allow Israel to build up it's military forces and use a heavily dominate security force to secure her border. Even then, terrorist groups located in Palestinian lands cannot be reigned in by just a security force, and so the conflict would not truly end. Remember, on one side, they are asking for the destruction of a people group on all cost, while the other side is trying to defend herself.
Has the Arab-Isreali conflict persisted since 1948? It not only has persisted, but grew worse over time.