If you are referring to mass balance with respect to total peak area by normalisation method, then this technique may give misleading results, because degradation compounds can yield a similar area. The best technique we have found is to scan each peak and determine purity (PDA Detector with Shimadzu LC solution software)
I agree with George. I have developed SI assays previously without taking mass balance into account. I think even most pharmacopoeial methods don't. You never know what breaks off and how it affects UV absorbance. Your method should be validated like any LC method, including peak purity, precision, linearity and accuracy for major degradants if possible.
I agree with previous comments of Christian and George, I think you do not need to any mass balance method for stability indicating method by HPLC. I think, after you incubated your samples in certain of time with HCl, NaOH, H2O2, UV, etc., you should analyze your sample(s) by HPLC. The target peak(s) should be evaluated regarding its identity (compare to fresh standard) and its purity (not contaminated with the possible degradation product(s)), and its concentration can be estimated by comparing its peak area after degradation experiments and its peak area of fresh solutions (with same concentration). The possible degradation products can be valuated by the presence of new peak(s) after stressed experiments. If you used MS as detector I think you can predict the chemical structure of your degradation product(s). If you used only DAD as detector, it could be you cannot see the degradation product9s) (it could be not UV active compound)
Mass balance can only be calculated after all the degradants have been isolated, identified and synthesized. When you have reference standards for most of the major degraded compounds you can then calculate mass balance. I have done this and it is a huge effort and requires some talented synthetic chemists to provide the references.
Richard brought up an excellent point: you should strive for understanding your chromatogram, so it is very helpful if you can calculate relative response factors for your main impurities. However, to find out what your main impurities are, you need the response factors! You will typically never achieve full mass balance but when you lose 1 % API, you should have an idea where it goes!
You may want to have a look at employing a CAD detector in addition to your current one for validation only: see link. It is less dependant on relative response factors and gives you a good first idea, what your prominent impurities are.
So the short answer to your question is: yes, you should have (some sort of) mass balance to be safe in terms of validity.