Fourier Synthesis With Varying Frequencies Over Time
You might want to have a look at the overlap-add (http://en.wikipedia.org/wiki/Overlap%E2%80%93add_method) and overlap-save (http://en.wikipedia.org/wiki/Overlap%E2%80%93save_method) methods. But, if all you are trying to do is additive synthesis, you don't absolutely have to use the IFFT to generate your signal. 

You can set up a bank of $M \in {[1 \ldots N_{Osc}]}$ elementary oscilators of the form $x_m(n)=\alpha_m \times sin(\frac{2 \times \pi \times f_m \times n}{Fs}+\phi_m) $ where $m \in M, N_{Osc} \in \mathbb{N}$, $\alpha_m, \phi_m, F_s, f_m \in \mathbb{R}$ and final output $y(n) = \sum_{m \in M}{x_m(n)}$.

In this case, $\alpha_m, \phi_m$ are amplitude and phase coefficients for each oscillator at frequency $f_m$ and to make them variable in time, all you have to do is turn them to $\alpha_m(n), \phi_m(n)$, i.e. to make them dependent on time sample $n$. This can be an absolute definition, by actually defining a varying waveform or by using some form of interpolation to provide initial and final values for these quantities and let the intermediate values be calculated automatically.

This would work both for generating one sample at a time or a frame of samples at a time (by iteration) and would not have any problems with continuity.