If you have access to journals, check out Thomas Jay Nisley, 'From Pinstripe Wool to Ripstop Poplin: The President, Symbolic Politics, and the Salute', Journal of American Studies, 45, 1 (February 2011), pp. 131 - 144.

From the article:

Eisenhower, who had campaigned for President on the promise to end the war in Korea, traveled to South Korea as president-elect. Eisenhower wore a military cold-weather jacket while visiting the war zone in winter. Following this one event, Eisenhower never again wore military-style clothing, and he always wore a pinstripe suit or casual golfing apparel. Eisenhower was very sensitive to civil–military relations and understood the need for civilian control even in appearances... Eisenhower resisted any latent temptations to return the salute of military personnel who are required to salute the President. Subsequent Presidents, from John F. Kennedy to Jimmy Carter, kept their hands by their sides when military personnel saluted. This long-standing presidential practice ended with the election of Ronald Reagan. (p.140)

The article then cites Reagan's autobiography:

Finally, one night when Nancy and I were attending a concert at the Marine Corps headquarters, I told the commandant of marines [sic], ‘‘I know it’s customary for the president to receive these salutes, but I was once an officer and realized that you’re not supposed to salute when you’re in civilian clothes. I think there ought to be a regulation that the president could return a salute inasmuch as he is commander in chief and civilian clothes are his uniform.’’ (p.141)