Unfortunately, the bank may well have their own criteria for account holders, and may have internal rules that they will not hold deposits for non-residents. Or, perhaps it is to do with the type of account you are holding.
However, this has nothing to do with the tax position, but merely the bank's internal workings.
Why not shop around for other accounts with other banks, both here and offshore?
I am not a financial advisor and can't give investment advice.