South Carolina does not have a minimum filing requirement so you are obligated to file a state income tax return.
South Carolina says:
A nonresident individual receiving South Carolina income from wages, rental property, businesses, or other investments in South Carolina, must file an SC1040 South Carolina Individual Income Tax Return and Schedule NR Nonresident Schedule.
See Code Sections 12-6-1720 and 12-6-2220.
Additionally your question is unclear about whether the business and rental losses are South Carolina-based. If so, filing a state return will record your net operating loss for state tax purposes.
See: SC TECHNICAL ADVICE MEMORANDUM #87-6
