MSU vice-chancellor Ramesh Goyal said that Santosh was suffering from epilepsy and his death might have occurred due to that.
According to his roommates, Prasad was not keeping well for quite sometime. On Monday morning, when he did not return after a long time from the bathroom, roommates and the cleaning staff broke open the door. Prasad was a resident of Veraval and only son of Madan Prasad, who works with Indian Rayon.

Please explain to me what "keep well" means here.

Source : http://timesofindia.indiatimes.com/articleshow/4689356.cms
Prasad was not keeping well for quite sometime.

The expression seems to mean "taking care of his health."

These things vary by region and ethnicity.

My Jewish friends in the US typically say, "Be well," when parting. (Not always, of course.)

Christians or wasps would more likely say, "Stay well," "Stay healthy," "Take care of yourself."

"Not keeping well" isn't an expression I personally hear in the US.

In BrE, I am keeping well means I am staying healthy,
Basically, my health is OK.

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It is not AmE, but I suppose it means that he had not been healthy for quite some time.
 Avangi's reply was promoted to an answer.
People I work with over in India used the term "not keeping well" in place of what I would use "not feelining well". When someone is out of work because they are "ill" or "sick" (in the US), the guys in India will say he's "not keeping well"
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