Actually, technically speaking, the US hasn't been in a formal war since World War II ended in 1947. Yes, there have been military actions more or less continuously since then, but no declared wars. Which is a stupid distinction to make, but it is a distinction.

Anyway, in case I wasn't clear: it's not the declared war that matters, but the two years. There aren't supposed to be any army appropriations that last longer than two years (with the expectation that no war would last that long anyway, and if it did that congress would be motivated to continue funding it). The idea is that a standing army should be impossible in peacetime. A navy is fine--Article 1, Section 8, Clause 13 allows for a standing navy--but clause 12 prohibits appropriations lasting longer than two years, and clauses 15 & 16 give them the militias of the states as the bulwark against "insurrections" and "invasions." (Unfortunately, it does also give Congress the right to use the militia in the pursuit of "execut[ing] the laws of the union," which is terrifying in a lot of ways.)

And actually, I was glib about "since before the ink was dry," but actually we fought every war of the 19th Century with mostly volunteers. A small army (only about 800 soldiers, at the start) was kept to guard frontier forts and national harbor batteries; in time of war, the militias were called up and formed the army (though the word "militia" fell out of use in favor of "National Guard" after the Civil War). Even after World War I, when the draft had ballooned the Army's size from 140,000 to almost 2.5 million, the drawdown began shortly after the war ended, and it was back down to near its prewar numbers by 1920. Around that time, our army was 190,000 strong, making it one of the smaller armies in the world; some estimates put it around 19th in size. When Hitler invaded Poland, the US Army was smaller than Portugal's.

But World War II was the turning point. The US Army grew to over eight million soldiers between 1939 and 1945, and though they were demobilized dramatically quickly (some historians say too quickly), the size of the Army hasn't dropped much below a half-million since. And that size standing military is tough to justify with just guarding harbor batteries; there aren't any more frontier forts, so if you maintain appropriations for more than 500,000 active duty soldiers every two years for almost a century, I think the founders would have some issues with that.