Do Fixed Bias BJT 's have a cut in voltage?
The MMUN2211LT1 already has a base resistor of 7~13kΩ with an hFE of 35 ~60.

If you apply 2.5V to base resistor it will saturate to 0.2Vmax with 5mA collector current.

added- -
I read the above in the product spec. Have you read it?
My analysis of this switch is as follows;
Output 5mA for input 2.5V/10kΩ nom = 0.25mA which translates to current gain of 20x which is typical for a saturated switch. 
5x is common for high current switch.



So apply more base voltage to this device and remove the external base resistor.