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I did a bit of work on this including a paper stowage plan and all, and on a 43 footer for four people, it worked out to about six months. However...
Realistically, the vessel could not stay at sea all that time without fresh supplies. Phsyically, it could be done quite easily (with a water-maker), but even on relatively short journeys (two weeks) we have ended up just popping into places, for things like fresh milk, fruit, and things we just fancied.
Modern dried foods, tinned fruit, re-constitutable foods, and other such stuff are a Godsend to a cruising yacht, but in my experience, we have always forgotten something, and sometimes just fancy something not on board.
Towards the end of a trip, we often used to end up eating some pretty wierd and wonderful combinations though.
I suppose if planning a trip into the Antarctic, a survivalist venture or something, you could load more aboard, but you might then be deck-stowing gear, and you'd have to watch the weight as well.
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