Am I using this transistor improperly?
Yes, it is absolutely ok to have transistor always on. There's nothing wrong with that. However, you must look at power dissipation. Transistor is able to dissipate only certain amount of heat. This amount is specified in datasheet. It depends on amount of passing current, voltage across colector-emitter and that depends on base current. If you dissipate too much heat, transistor gets hot, and you will need to use heatsink.
Look at the voltage across colector-emitter. If it is not close to 2V, than you probably need to increase voltage on base (or use lower resistor). Otherwise you need heatsink.
UPDATE:
I recommend to use MOSFET instead of TIP120 which is NPN Darlington. MOSFET dissipates much less heat, it is much better for power switching.