How big is your tank? what temperature is your tank at...do you have a heater? Sometimes bettas get too cold and their metabolism slows down and they will not eat. How often do you clean our water as well?
Not eating could also be a result of illness, check for change of color, lethargy, discolored gills, lesions or bumps, strange spots, look at his gill movements are they rapid or extremely slow? Is he swimming normally?
Check for other symptoms of illness, but if he has cold water that is probably it.