Interpretation of FFT result when frequency is an exact multiple of frequency bin
Short term FFTs apply a windowing function at moving intervals, do an FFT, and average.  In this case, the interval with which the windowing function is applied is phase-locked to the signal, so what tends to be a process averaging out over the integration time no longer does.  You get the FFT of this intermediate product without averaging and it depends on just where you locked phase what comes out.

However, you did not state just what kind of signal you are using.  For a sine wave, I still would expect the result to be pretty close to a single peak.  It may be that this peak is absent due to fixed point overflow since the analyzer might not be prepared for the full concentration of frequency.  If that is the case, just reducing the amplitude might change the outcome to something more expected.