I know that first question may have sounded stupid, but, yeah, been there, done that, with propane and charcoal rigs. Just need more info to figure this out.
How long does it burn, and does it go out with the door open, closed, both...maybe it flames out right when you open the door? (some do this, so you have to open/close it slowly)
Have you tried closing the burner valve, tank valve, waiting about 30 seconds, then slowly reopening the tank valve and relight the burner? Sometimes the excess flow device in the tank valve will stick shut if it senses high flow. If you have another tank you may want to try that tank, just to verify if it's tank valve related or not.
Disconnect and check the tank and regulator/hose connections for blockage from dirt, critters, ice, etc.
There is a slim chance that the gas regulator on the smoker has a stuck valve, partially seated and just allowing enough gas through for a light-up, then it goes out due to low gas flow/pressure...again, slim chance, being it's new, but I have probably seen stranger things happen.
Eric