I would not say America has always supported Israel in its fight against its Arab neighbors but they certainly have almost always supported Israel. I say this because in the 1956 Suez War, Israel, the UK, and France fought against Egypt but at the time, the American President Eisenhower was not supportive. Also President Obama had some disagreements with Israeli Prime Minister Benjamin Netanyahu; the two leaders clashed regularly over issues like settlements and Iran.
Some reasons for American support include serious patronage for Israel among the American public, the influence of the pro-Israel lobby, the presence of a stable democracy in the Middle East which also helps to serve as a buffer against Russian influence, and a common interest in fighting terrorism.