Banks at present are not allowed to offer more interest to NRE accounts than those prevailing for residents. However, since interest rates may go down after two years, your question of whether they will break FD or continue with the same FD are important.
There is a clarity with respect to FCNR B Account that the banks can continue to give the same rate of interest.even after you become resident, till the maturity of the fixed deposit. However, with respect to NRE Account such clarification is not available.
Therefore you are requested to get the confirmation in writing from bank that they will not break the FD after you become resident and keep your FD only with such bank.
So far as taxation is concerned, since only a person resident outside India as per FEMA can get the exemption on interest on NRE account, you may not qualify for tax exemption for the interest post becoming resident (whether you break the FD or not) even if you do not change your status in bank but you are resident as per FEMA. You may check as to how to remain non resident for longer time as per FEMA to extend the exemption.
I appreciate your question and since this is a very common problem, hope that above mentioned clarification will help.