"Is that true? Are you saying that's a Tony eligibility rule? I guess I can't think of a case when a show has been revived less than three years from the original, or even another revival, but it surprises me that they'd have a rule like that. It seems more just like common sense, that producers SHOULDN'T revive a show a year after the original. Theoretically, if some other producer foolishly decided they wanted to do a revival of The Last Ship this fall with new direction, design, etc. wouldn't that be considered an eligible revival? "
In the unlikely event that something like you described happened with The Last Ship (or any show), the producers could always petition to be considered. But, that's such a far-fetched scenario to imagine any producers picking up the rights and re-opening an entirely new production in such a short time span that there's no reason to even address it until it happens.
I've assumed the rule regarding how much time has to pass between closing of one production and the opening of the revival was put in place to deal with tours that are doing "return engagements" (Hair and Fela!, for two recent examples), and shows that close for a short period to do a major re-tooling and overhaul of the show and then re-open in the same season they close (there were rumors that the producers of The Scarlet Pimpernel wanted to be considered as a revival when they closed at the Minskoff in May of 1999 and then re-opened that fall at the Neil Simon).