Try preheating the cooking chamber slightly maybe?
If you have plenty of exhaust and intake, dry wood, and know how to start a fire, IMO you have to be right on the draft... wind could be causing the issue. if you are cold smoking and heating isn't an option, you could try forcing a draft with a fan, but if the issue persists, maybe change where your exhaust is?
My grandfather's was dug into the side of a hill with the stove down near the barn... I don't remember draft issues but the smoke house was on the east side of the house and wind was primarily westward so it was quite protected and the stove pipe had a decent incline. Pretty ideal and my only experience so I don't have much to offer on draft issues