Even if Carter stood solidly behing the Shah then how could he have kept him in power? The man had no support among his own people.
True ... further, as I recall, the Shah was having health issues that required treatment outside Iran. This was perceived as an opportunity by his enemies to move towards his overthrow. Carter, in his ineptness, certainly accelerated the process ... however, it ultimately cost him his presidency when the American Embassy was attacked and the hostage situation drug out for well over a year.
"The man had no support among his own people."
BS!
That's what you believed from taking in what the communist loving media of this country fed you.
Talk to an Iranian that escaped and came here when that was going on if you want the truth.
Any communist needing help in the world is supported by Carter, even to this day.
I recommend this book
http://www.worldcatlibraries.org/wcpa/top3mset/f24e826a2df4263da19afeb4da09e526.html
Through repression and intimidation, like any other normal Muslim leader, from Mubarak to the House of Saud.