I recommend you file a MO return to report the real estate activity.
The "Who Must File" instructions for MO non-resident returns is a bit vague in defining "Missouri income". It doesn't distinguish between gross income, net income, taxable income or profits. (See attached text fro MO DOR website)
The conservative approach calls for using gross income as the measure of whether or not you are required to file a return, You wouldn't owe MO taxes because of the net rental loss.
Here is the compelling reason for reporting the MO rental loss. When you sell the property, you will have to report the sale to MO. Carry-forward passive losses, if any, would reduce your taxable gain (keep in mind recaptured depreciation). If you don't file MO returns in loss years, MO may very well disallow using carry-forwards when you report the sale.