Figment:

If everything is set up properly you should only need to have the choke engaged for starting. After that, the choke should be FULLY open.

If you're having a problem running the engine without the choke disengaged after you've started...you probably are starving the engine for fuel.

Check the basic things:

Once the engine is warm and with the choke FULLY off:

Adjust the idle mixture screw - turning the screw clockwise [inward], this will make the mixture richer (the screw actually adjusts the amount of air it let's in).

Check fuel filters.

Check gas tank vent for obstructions. (If when you open the gas tank cap and there is a sound of air being sucked into the gas tank - you have a venting problem.)

Check fuel pump efficiency.

Check ignition timing.

Good Luck!
Steve Kaminsky