Why would Humphrey lose after a single term?
What could he have done much differently than Nixon and succeeded in doing so?
I doubt that opening up to China would be happening with him. OTL, for that to happen, you had to have two powerful guys go against the State Department establishment in a quest so cynical and unheard of at the time that it involved Henry Kissinger basically stowing away to China. Humphrey was firmly in the Cyrus Vance Establishment diplomatic camp, and wanted better relations with the Soviets based on post WW2 idealism rather than cynical understandings of American power and its limitations. There'd be no Chilean coup, which might have negative Cold War consequences in South America, as well.
He also would not have been able to stop the Vietnam War other than possibly by packing up and quitting, which would not at all be good for him politically. He might have just done that and allowed South Vietnam to go through the tribunals and re-education camps 5 years earlier than OTL.
He was not corrupt, kind of a rarity, nor was he dirty. That would allow him to escape Nixon's issues OTL. But he would not have been a better President.
The moderate and successful legislation that Nixon and Capitol Hill worked on during his tenure would likely still come about, and that'd help, but Humphrey was out of his depth on other things.
And keep in mind that the 1972 electorate was one of the more Conservative ones in the century when you look at the demographics of who was voting. Not really sure why this was, maybe it was that the radicalism of the era dissuaded leftists in the US from going to the polls. I think a Humphrey Presidency would be a one term one, especially when he fails to deliver the promised goods, as he clearly would have.
Maybe I am being too harsh on the guy. He might have, like Obama, gotten to the Oval Office and understood some practical realities that were not as apparent on the campaign trail,and governed more as a centrist, and like Nixon, with a more robust and intuitive foreign policy. But I'd have to say that its not likely.