I have the big rounded shape that I wish to cut on sides with a boolean difference. But it fails.
Here is my file: booleandifferencefail.3dm (370.8 KB)
Your extruded oval exists of 2 objects.
see 2nd image.
Extract both surfaces and MergeSrf them. Them join all together again and try again 
I just see that the top part also exists of 2 parts… Merge these first and then with the lower one.
While MergeSrf them put smooth = no
The problem is that you try to booleandifference an object that crosses 2 surfaces.
EDIT:
A more clear Image:
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