Take Comfort in What You Kniw, by Corpus Invictus, is a multi-chapter, AU fic where Spock suffers from agoraphobia: http://archiveofourown.org/works/715652/chapters/1324993

Convalescing, by Charlotte Frost, is a quite long TOS fic set aboard ship, after Spock becomes extremely ill with flu: http://ksarchive.com/viewstory.php?sid=3489

A Breath Beneath Bitter Sands, by Arisprite, is also a TOS fic set aboard ship: https://www.fanfiction.net/s/5459103/1/A-Breath-Beneath-Bitter-Sands

Sorry, they're all sick Spock! I've read lots of shorter sick Spock or sick Jim, but don't really keep track of them.
Celestial Fever, by Spinesless, is a sick Kirk one, but it's more McCoy-takes-care-of-Jim-in-sickbay than K/S. https://www.fanfiction.net/s/9479433/1/Celestial-Fever

In Fever Dreams, by mattmetzger, is part of the Progression series, but you could read it alone, I think: https://www.fanfiction.net/s/6358797/1/In-Fever-Dreams

Also by mattmetzger is What Are The Odds, followed by Mid-Afternoon and The Fierceness of a Storm - very angsty hurt Spock, but beware - the series is unfinished (and never likely to be finished) so the happy ending isn't there. No-one dies, but it's not a happy ending: https://www.fanfiction.net/s/6677186/1/What-Are-The-Odds