Shirdi Sai Baba gave up the body by giving up food for around two weeks

Above pic: The Great Shirdi Sai Baba. 'Sabka Maalik Ek' (The boss/master of all is ONE) i.e. God is ONE for all people of various faiths (and no faith). [Courtesy: http://www.saiamrithadhara.com/uniqueinfo.html]

Above pic: Shirdi Sai Baba with devotees. [Courtesy: http://www.saiamrithadhara.com/uniqueinfo.html]

From the official biography/account of Shirdi Sai Baba: Shri Sai Satcharitra (English), http://shrisaibabasansthan.org.in/publications/shri-sai-satcharitra/english/shri-sai-satcharitra-english-chapter-42/ :

The readers up till now heard the stories of Baba's life. Let them now hear attentively Baba's Passing away. Baba got a slight attack of fever on 28th September, 1918. The fever lasted for 2 or 3 days, but afterwards Baba gave up his food and thereby He grew weaker and weaker. On the 17th day, i.e., Tuesday, the 15th October 1918, Baba left His mortal coil at about 2-30 p.m. (Vide Professor G.G. Narke's letter, dated 5th November 1918, to Dadasaheb Khaparde, published in "Sai Leela" magazine, Page 78, first year).

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Ravi: I think that's the way many spiritual masters give up the body. They simply stop eating! I think that's a great self-controlled way to give up the worn-out body, and so very fitting for fakir/renunciant type spiritual masters, or even fakir/renunciant type spiritual aspirants.

The above-mentioned link, http://www.saiamrithadhara.com/uniqueinfo.html, has great additional photographs and portraits of Shirdi Sai Baba with some background information.