Besides the reasons listed above (incumbency aka FDR fatigue, certain demographics swinging against FDR, ancestral GOP areas shifting back, etc...), a large part of why these states:
But he lost Indiana, North Dakota, South Dakota, Nebraska, and Kansas in both 1940 and 1944 despite doing a lot during the dust bowl. Same with Colorado strangely enough
...swung against FDR because their economies didn't get much benefit from FDR's New Deal and failed to fully recover. ND, SD, NE, and KS (excluded from your list is Iowa which also swung against FDR) began to swing against FDR in the 1936 elections and just continued doing so in 1940. Part of the reason is simple: those states economies were worse off in 1936 relative to the nation as a whole as evidenced by their continued decline in income:
It should be noted that FDR's powerful aides James Farely and Harry Hopkins conspired to strategically disperse relief funds in the run up to the 1936 election. Spending on government transfers jumped significantly in 1936 after remaining steady from 1933 to 1935 and most New Deal spending ended after the 1938 midterms. If at the peak of New Deal spending in 1936, states like ND, SD, NE, IA, and KS couldn't recover then they just simply voted against the incumbent.
Did they recover from the Great Depression sooner and thought the New Deal wasn't needed anymore?
The answer is the opposite: Plains area states got no benefit from the New Deal and economic hardship continued under FDR while most of the rest of the country benefited and recovered. In response, they just simply voted against the incumbent in 1936, 1940, 1944. Very similar to what happened in Iowa during the Reagan/Bush years.