Hi, Kathy. Can you tell us more about what seems to be happening to your shutters? Words like "crooked" and "sagging" make it kind of hard to figure this out since they could be moving in so many different directions. What kind of hinges do you have and do they appear to be OK? Are your shutters made with mortice and tenon construction? Are the shutters original to the house?
60 years is a long time for wood to go. Paint protection is not as complete as it might be on siding and window frames since there are a lot of places that water can enter. Usually different varieties of wood are used for shutters than say siding since the shutter wood has to mill well also.
Give us a little more idea what's going on and we may be able to help.