You need to report your SC rental real estate activity.

From the SC DOR website: A nonresident individual having South Carolina rental property as an investment in South Carolina should file Form SC1040 and Schedule NR - Nonresident Schedule. Rents received from the rental of real estate, less all related expenses, are allocated to South Carolina providing the property is not used in or connected with the taxpayer's trade or business. 

See Code Section 12-6-2220.

There is another compelling reason for reporting the SC rental activity. When you sell the property, you will have to report the sale to SC. Carry-forward passive losses, if any, would reduce your taxable gain (keep in mind recaptured depreciation). If you don't file SC returns in loss years, SC may very well disallow using carry-forwards when you report the sale.