A high tier Sith Lord can master the art of going with out sleep for insanely long periods of time. Your average person loses sleep and they get cranky. A Sith Lord goes without sleep and feeds on the crankiness for Dark Side power. There is still physical exhaustion, but you can ward that off with the Force up to a point. This is very useful if you want to live a secret double life, but contributes to the Dark Side eating away at your vitality.
Palpatine's master, Darth Plagueis (aka Hego Demask), actually was murdered by Palpatine when they were celebrating Palpatine's securing the nomination for Supreme Chancellor and Palpatine got him very drunk. Plagueis had survived an assassination attempt and had been without sleep for actual years, so when he got drunk and because he was already very tired, he forgot to stay awake perpetually and took a nap. The Dark Side then literally whispered in Palpatine's ear to murder him, and it happened. This was all going on while Padme, Anakin, Qui Gon, Obi Wan, Jar Jar, and R2 were flying back to Naboo in TPM, and is documented in the novel Plagueis.
