I agree with Mr.Prasad. The FD has to run the whole period only if the First named or the Other wish to pre-close. The very purpose of Either or Survivor is to reduce this problem.
If the Survivor gives the Death Certificate and requests to the Bank to convert it in his/her name, the Bank has to do it.
Having become sole owner of the FD it can be pre-closed.
Even when both signataries are alive, if they both sign, the FD can be pre-closed.
If you Google search for the ruling by RBI, you will get the circular.