Yes, both are fine.
I don't know what the other two commenters mean by 'spoil' meaning that you did something wrong. It's not. A spoilt appetite is simply an appetite that is not as strong as it should be.
October 27, 2017
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Yes, you can use both. As Georgie said, "spoil" implies that you did something wrong, like eating junk food right before dinner. I would also add that "lose" could imply you're not hungry because you feel sick.
October 27, 2017
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Yes you can use both. 'Spoil' implies more that they're doing something wrong
October 27, 2017
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