Inline water heater temperature floor?
Tankless/on-demand (is this the same as inline?) water heaters only heat if the water flow rate is above some minimum, typically around 0.5 gallons per minute. As the water temperature is made more cold, less and less hot water is going into the mix. At some point, the hot water flow decreases below the threshold and the water heater turns off, yielding cold water flowering through the hot water pipes.

Your water heater may have an adjustable flow rate threshold, and if so, it could be decreased. Another solution would be to decrease the temperature setpoint to be closer to the desired final temperature (though you may need the hotter water for dish or clothes washers).