You definitely have to be careful. Another thing you can lose is a reduced deposit. And if the new offer does not have the reduced deposit, you can lose the entire cruise if you do not pay the new deposit.
I do remember once finding a reduced fare, but our TA warned that without paying the now extra on the deposit, they would cancel the cruise reservation. Since it was worth it (and the extra deposit would have had to be paid eventually anyway as part of the fare), I added the extra funds to the deposit.