He had a concussion previously (last April). Even when a player is 100% from a concussion, it still lingers for a while after. People forget, that it took Crosby a solid calendar year after his concussion to be back to Sidney Crosby. Even with his foot injury in December, it's possible that still isn't fully healed.
It came out Saturday that Zaitsev had the flu. IIRC he was still practicing last week. So really it has only been 2 days, 4-5 at most. While significant symptoms are usually only around for 2-3 days, the weakness, fatigue etc can last anywhere from 3 days to 14 days depending on the severity.
It's likely this is just a severe case of the flu, but they are doing more tests to confirm that, and ensure it's not anything more serious.
I myself was sick beginning 2ndish, and today is the first day where I have like no symptoms whatsoever. There's a lot of people who have been getting sick this year and carrying symptoms for weeks, rather than days.