For Direct-Sequence Spread Spectrum, can we reduce the transmit power of the signal to maintain a fixed BER?
BER depends on your E_b/N0. You need to keep that constant if you want constant BER.
Now, you don't say how your comparing your DSSS system, but it would make sense to assume that your symbol rate constant, thereby increasing your bandwidth by the spreading factor, and keeping the duration of a symbol constant.
In that case, Energy is still the product of power and duration, and the latter stayed constant.