Not a historian on the subject but I majored in political science. The main reasoning was to remove them from the realm of politics. If they have to vie for re-election or re-appointment it would make their decisions, like any politician who wants to keep their job, beholden to the officials appointing them or the public. Ideally, a judge is to remain impartial and the only influence on his decision should be the law, more specifically, the Constitution.

Well, this is delightful! I love seeing questions in my specialty. I'm happy to give you a thorough reply. First, I don't take your question as political at all. It's important that we're able to discuss the legal system without it necessarily devolving into politics. I will strive to do the same in my answer.

Now, on to the subject at hand, Article III of the Constitution creates the federal judiciary. Due to a compromise at the Convention, the Article creates only the Supreme Court, and allows Congress to create and abolish the lower federal courts at will. Congress's power to actually do that is quite a complicated subject, and beyond the scope of this answer, but I'm happy to discuss it later if you're curious.

Anyways, as I was saying, Article III, Section 1 of the Constitution sets the tenure for all federal judges. It states:

The judges, both of the supreme and inferior courts, shall hold their offices during good behaviour, and shall, at stated times, receive for their services, a compensation, which shall not be diminished during their continuance in office.

"Good behaviour" means for life, barring impeachment. As to your question about whether this was the Framers' intent, then, the answer is a firm "yes." This is the way it's been since the founding. As a sidenote, because the qualifications of a federal judge are constitutionally defined, a Justice of the Supreme Court, or a Judge one of the twelve Courts of Appeals, or one of the many federal district courts, is referred to as an "Article III judge." Note that bankruptcy judges are not Article III judges. This matters for many reasons, and has been a subject of recent litigation (see, e.g., Stern v. Marshall).

Back to lifetime tenure, /u/Shaqueta correctly points you to Federalist No. 78, by Alexander Hamilton. In addition to the passage he/she quotes, in that letter, Hamilton-as-Publius writes that:

If . . . the courts of justice are to be considered as the bulwarks of a limited Constitution against legislative encroachments, this consideration will afford a strong argument for the permanent tenure of judicial offices, since nothing will contribute so much as this to that independent spirit in the judges which must be essential to the faithful performance of so arduous a duty.

In other words, lifetime tenure "during good behaviour" was explicitly intended by the framers to be what Robert Caro would call "armor," bolted on to the judiciary to insulate it from the political vagaries of the world. He considered this armor especially important because, presaging the power of judicial review, he viewed the Courts as likely to come under attack whenever their duty to enforce the Constitution brought them into conflict with a coordinate branch of government.

The significance of this protection would prove critical mere decades later, when the Democratic-Republicans, having swept into office in a landslide with the overwhelmingly popular third President Thomas Jefferson, sought to purge the judiciary of judges and Justices from the opposing Federalist party. Lifetime tenure meant that Jefferson could not succeed in this venture, which would have turned the entire federal government, as if on a dime, into a one-party system. Jefferson tried his best to do this anyways: he sought to impeach lower judges, and ultimately Supreme Court Justice Samuel Chase, and was only defeated when a bare majority of the Senate, persuaded by Vice President Burr and Chase's attorneys, concluded that Article III judges should not be impeached for their opinions alone, or in fact, for anything short of an actual crime. No such allegations were made against Chase. Taking the entire exchange as an example of the Senate's independence, and its unique ability to stand up for the independence of a coordinate branch, Robert Caro writes:

Chase's conviction would have established a precedent that would have undermined the independence of the courts, and thereby endangered justice itself.

The quote, and the narrative description, is (oddly enough) from chapter 1 of Volume III of Caro's Years of Lyndon Johnson, titled Master of the Senate. In it, before turning to the subject of his biography, Caro narrates at length the Senate's triumphs and failures over its 200 years of existence. It's a great prelude, and if it suffers from Caro's use of the incident as part of a theme rather than a subject in its own right, similar facts and discussions can be found in Gordon Wood's Empire of Liberty, chapters 11 and 12.

Minor clarification: Supreme Court justices (and many other federal judges) are appointed by the President with the "advice and consent" of the Senate. They aren't elected, unless you count the Senate voting on their appointments an election.