Why is "viva" pronounced `/ˈvaɪ.və/` in the academic sense?
Solution 1:
"viva" meaning "long live" is borrowed from Italian or Spanish, and approximates the pronunciation of the source languages. (IIRC, the Vauxhall Viva car had the same pronunciation, though I don't have a source for that.)
However, "viva", short for "viva voce", meaning "oral examination", is borrowed from Mediaeval Latin. Pronunciation rules for Mediaeval Latin words are not the same as those for modern Italian and Spanish, though I don't know when or why the long 'i' prevaled for this sense.
Source: http://dictionary.reference.com/browse/viva