Ike went from winning Missouri by 2% to losing it by 0.2%. The swing isn't that significant.
This is like asking "why did FDR win Michigan in 1944?" Yes, he had lost it four years earlier (and the Midwest generally swung right in 1944), but it's a matter of a 1-point win versus a 0.3-point loss.
Obviously the swing wasn’t huge but it is a bit of an oddity nonetheless.
Perhaps the explanation about parts of the rural midwest swinging against him explains it, but even then I’m not sure why. Was there some kind of agricultural crisis I’m not aware of?
Apparently
Ezra Taft Benson, Eisenhower's Agriculture Secretary, was deeply unpopular in the Farm Belt due to his opposition to subsidies and price controls as socialist. (Benson was outspokenly anticommunist and would go on to endorse the John Birch Society.)
