latching a single transistor

I thought this would work as a latch, but it doesn't: I've got a single 2n2222a npn transistor in an emitter-follower circuit: +12V (unswitched) to the collector, emitter goes thru a 10K resistor to ground, and switched +12 to the base thru a 330K resistor. Also, the emitter is connected back to the base thru the same 330K resistor. Therefore, I reasoned, once the switch is turned on applying +12 to the base, the transistor will turn on, and then when the switch is turned off the transistor will stay on (the latch part) since the +12 (unswitched) is still applied to the collector, and the base should keep getting the +12 via its connection to the emitter; i.e. it will latch on. But it doesn't latch. It turns on when the switch is turned on, and turns off when the switch is turned off. You can probably tell from this I'm somewhat of a novice at this stuff. So why doesn't it work?