When will Palestine just give up and become part of Israel?

we'll find out if that happens

Never. They've been fighting occupation by Israel since Israel was given its independence and sovereignty over the region where they, the so-called Palestinians ("so-called" because it's not their actual name but an exonym, a name the Roman Empire made up) were living and had been living for centuries was handed over to a government of Jewish colonists that defined itself as a "Jewish state" and thusly called itself Israel since 1948. Before that, the so-called Palestinians were fighting the imposed occupation by the the British Empire, which had conquered the the region in 1917 from the Ottoman Empire during WW1, which then was granted sovereignty over it in 1920 via the San Remo Conference, and which then in 1922, by way of a League of Nations charter, imposed a Jewish population by making it a colony for the the British Empire and other League of Nations countries to forcibly relocate Jews to, which is how the first Jews returned to the region in almost 2,000 years, ever since the last Jews were driven out of Jerusalem by the Roman Empire in 73 AD and continuously kept out of Jerusalem by the subsequent Byzantine Empire (an Orthodox Catholic empire) and the subsequent Ottoman Empire (a Muslim empire).

People who have been fighting foreign occupation and foreign colonization for nigh onto a hundred years now aren't ever going to give up, especially given that the last time they fought against Jewish occupation, they fought against it for over 2,400 years. They have maintained their claim to the region as their homeland and maintained a population in the region since they became its first settlers circa 3,800 years ago, several hundred years before the Jews invaded it circa 3,400 years ago and got expelled from it 1,947 years ago. The so-called Palestinians were the first settlers of that land and have been there for now 3,800 years, despite literally thousands of years of efforts to oust them from it, so I wouldn't expect them to ever give up. 

By the way, a more appropriate name for them would be Canaanites, but even that would be a misnomer since it at the very least is a Hebrew-ized version of what the people were called based on a Hebrew-ized version of the land's name Canaan. Philistines came later and were a lot harder to conquer, which led to the Jews genociding the Philistines. You can read about this in 2 Samuel of the Bible or in the Tanakh. But so hated were the Philistines, Jews started pejoratively calling all native inhabitants of their land "Philistines," a misnomer not unlike how European settlers in the Eureopean named Americas have called the native inhabitants "Indians," even though they're not really from India. Anyway, Jews calling natives Philistines pejoratively, the common noun "philistine" carrying over as a pejorative in English for someone who is hostile and smugly backwards (e.g., proud of being stupid and uncultured and looking down on anyone and everyone who is), led the Romans to mistakenly think that that's what the natives were really called, so the Romans adapted the name "Philistine" use by Jews for natives into the place name the Roman Empire imposed on the region of Palestine, which it did to serve as a constant reminder to Jews that they weren't the native inhabitants, either, and to propagandize the notion among natives that the Roman Empire had liberated their homeland from the Jews and, taxes aside, handed it back to them-- again, not realizing that the name Palestine was based on a misnomer that is every bit of a misnomer as calling indigenous peoples of the Americas "Indians."