Why do some people undergo sudden savant syndrome?
Savant syndrome can be congenital or acquired.[1,2] The acquired savant syndrome can occur in people with stroke, head injury, and even some degenerative diseases (such as dementia) that affect the left fronto-temporal lobe. [1] Transcranial magnetic stimulations of this area, which can cause inhibition in this area, can also elicit these kinds of unusual capacities too, even though only transiently. [3-5] So, there is a theory that the extraordinary skills of savants, such as calculating, memorizing, and performing music, exist latently within us all but are not normally accessible because there is inhibition from some areas, especially the left fronto-temporal lobe. 


  Snyder and Mitchell (1999) have argued that the extraordinary skills of savants, including mathematics and drawing, are within us all but cannot normally be accessed without some form of brain damage. It has also been argued that such skills can be made accessible to normal people by switching off part of their brain artificially using magnetic pulses (Carter, 1999). Using repetitive transcranial magnetic stimulation (rTMS) to interrupt the function of the frontotemporal lobe, a region of the brain implicated in the development of savant skills (Miller et al., 1996,1998), we tested this hypothesis. Here we show that savant-type skills improved in 5 out of 17 participants during the period of stimulation.[4]


So, lesions at the left fronto-temporal lobe can cause disinhibition of neural processes in some other areas and enable those areas to function with extraordinary capacities [3,4]; thus, some people can suddenly develop savant syndrome because there is an acute lesion, such as stroke, head trauma, and even transcranial magnetic stimulation, at the left fronto-temporal lobe (or other yet-undiscovered inhibiting areas) thereby releasing the latent savant skill.

References:


Treffert DA. The savant syndrome: An extraordinary condition. A synopsis: past, present, future. Philos Trans R Soc Lond B Biol Sci. 2009 May 27; 364(1522): 1351–1357doi: 10.1098/rstb.2008.0326. 
Wikipedia. Savant syndrome.
Snyder A. Explaining and inducing savant skills: Privileged access to lower level, less-processed information. Philos Trans R Soc Lond B Biol Sci. 2009 May 27; 364(1522): 1399–1405. doi: 10.1098/rstb.2008.0290. 
Young RL, Ridding MC, Morrell TL. Switching skills on by turning off part of the brain. Neurocase. 2004 Jun;10(3):215-22.
Snyder A, Bahramali H, Hawker T, Mitchell DJ. Savant-like numerosity skills revealed in normal people by magnetic pulses. Perception. 2006;35(6):837-45.