I have a rental property that has been depreciated every year since 2003. We no longer need the depreciation deduction. Are we required to keep deppreciating every year?

Yes, you need to keep claiming your depreciation as long as the property is still rented, until the basis reaches $0. 

Even if you don't need the deduction, you have to recapture the depreciation you took, or were allowed to take, when you sell the property. That means depreciation is not optional.