You have to be pretty damn anal to think using a colloquial term suddenly discredits all the other information in that article.
There is some validity to his point though. Every time I read the word "give-up-itis" I reflexively feel negative feelings towards the article. It feels as if they are trying to be funny but not in a good way.
If they had to come up with a "medical" term for "give-up-itis", I might guess it'd be "apathetic psychogenic decay", or else some Latinized phrase. https://translate.google.com/#auto/la/disease%20of%20giving%... yields "De morbo dare sursum", who knows.
I also suspect this research is early enough that it doesn't make sense to choose an official term and commit to it yet. I am in favor of people not polluting the namespace of terms with things that, upon closer examination, should have been named something else.