Some reports claimed the Shanklin - Ventor line was carrying as many as 250,000 passengers a year as of 1965. Professor E.R. Hondelink claimed the line could be returned to profitability should every passenger be charged a supplementary fare for the journey along Ryde Pier. Being the time when the railway board was ripping up branches left, right, and centre... it fell on deaf ears and the Ministry elected to close the branches.
A private society was set up with the intention to operate a private service between Cowes, Ryde, and Newport, and it even had the support of the county council, but the Railways Board ripped up the track, destroying the scheme.
Despite being electrified, an apparent internal memo of British Rail's suggested they wanted to put the remaining track up for closure in 1975... obviously it didn't happen.
(Source: The Great Railway Conspiracy - David Henshaw)