From Leviton web site:
RED LIGHT – The device needs attention. Your SmartlockPro Self-Test GFCI is engineered to regularly conduct an internal test (self-test) to confirm that protected power is available, offering an added layer of protection from electrical shocks due to hazardous ground-faults. If, during a self-test, the GFCI detects a potential problem, one indicator is a solid or blinking red light. In this case, simply press the TEST and RESET buttons to reset the GFCI. If the device resets, you’re good to go. If the GFCI will NOT reset or the solid or blinking red light continues, the device has somehow been compromised and must be replaced.
May be different brand, but sounds like it may be a bad outlet.