There is no such maximum limit for passage number for cell lines. Whenever you work with immortalized cell lines, it is advisable to freeze down stock of cells of early passage. When you work with these cell lines for bioassays, it is recommended that you use cells of lower passage, for instance, P10 - P25. When you no longer require the cells in culture, it is preferable to stop active cultivation. This reduces the potential for genotypic and phenotypic drift that could occur if the same culture was maintained and passaged continuously.
With increase in passage number, the cells undergo many changes which you could monitor. For instance, changes in morphology can occur over time which could be checked by visual appearance through microscope. You could determine growth curves for young and old cultures, and record the proliferation rates, which is likely to decrease with increasing passage.
Generally, working with cell lines of late passage for in vitro bioassays is not recommended because it may not provide results as expected.