When students ask for exceptions for extenuating circumstances we have to make subjective decisions regarding their situation. Write down your plans for these situations to ensure all students are held to the same policies. When new circumstances arise add them to your plans because having them written down will help you improve your consistency.
Example: Ill students receive a two-day extension.
See this and related tips as a Tip Sheet: http://csteachingtips.org/tips-for-reducing-bias