Holding bonds to maturity vs. selling them and buying new bonds doesn't actually change the financial result. You could equally say "just sell them and buy new higher-yielding bonds and there's no issue," since the resulting yield over the whole period would be equal.

Whether or not there's an issue depends whether your investment horizon matches your bond duration, or alternatively, whether you're comfortable with (or even aware of) the amount of rate risk you're taking compared with the return you're getting.