Residential rental real estate will almost always show a loss *on paper* a tax filing tome. Especially if your have a mortgage on the property. When you add up the deductible expenses of mortgage interest, property insurance, property taxes and the depreciation you are required to take by law, it is very common for those four deductions alone to exceed the rental income for the entire tax year. Add to that the other allowed deductions such as repairs and maintenance, and you're practically guaranteed to show a loss. This loss gets carried over to the next year where they can be realized *if* you actually have a profit. Since that generally doesn't happen, those losses carried over just continue to grow each year. You can't actually realize those losses until the tax year you sell the property.
It's a good idea to file a state return anyway so as to document with the state your carry over losses every year. Then when you sell the property those losses can be used to offset the taxable gain realized, if any. By not filing a state return every year, the potential exists that you could be audited in the y ear of the sale and required to "prove" your losses. While you very likely will be able to prove it, you'll probably find the hassle of doing so is significantly greater than having just filed state returns each year anyway.
Another possibility (though I've never heard of it myself) is that if the state is aware of your rental income (and they are if your renter qualifies for and applies for the state "renter's credit" if offered by the state) and you don't file the return, then the state may consider 100% of the rental income fully taxable and send you a bill that will include late fees, interest and non-filing penalties if the state has such a thing.
I don't know if GA offers a credit for renters or not, myself.
