The temperature difference between the inside and outside of the flue is what brings air into the stove. The larger the temperature difference, the stronger the draft.
So the chimney creates draft, and everything else reduces draft. Connector pipe, elbows, spark screen, even the resistance of the shape or baffles in the firebox are resistance in the system, the damper being the variable resistance. So you can see why smaller diameter pipe increases the resistance as well as not leaving enough heat escape to increase the draft. Here's what the negative pressure from draft does;
. When the atmospheric pressure is high, you have higher pressure pushing the air with oxygen into the stove to fill the void created by the chimney. The higher the altitude, the less pressure on a good day...... When a low pressure area moves over the stove intake, there is much less pressure to push oxygen into the stove. The larger the air intake, such as leaving the door open, the more square inch area the atmospheric pressure has to push in with. So larger outlet for more heat to rise through, and larger intake for the lower atmospheric pressure to use to get in.
To give you an idea of how minute the negative pressure is, the lowest pressure is at the stove connector measured in inches of water column.
1/2 PSI is about the normal pressure of propane line pressure for an indoor appliance. This is 11 inches of water column. Natural Gas is about half that, which is less than your breath. A U-tube manometer is used to measure this low pressure, which is simply clear vinyl tubing bent at the bottom in a U shape. Add water in the tube and it will find its own level. If you put a ruler behind it, when pressure is applied to one end, the other left open, the pressure will displace the water pushing it down on the pressure side and the water comes up the same amount on the side open to the atmosphere. You add the two together (rise and drop) and the total you get is inches of water column. So 1/4 PSI will move the water about 5 inches up one side and 5 inches down the other. This is the difference between the pressure side and atmospheric pressure at any given time.
Your chimney should be capable of producing .045 inches - notice that is decimal zero four five of an INCH. That would move the water 1/2 that much up and down the water tube scale. We're talking minute pressure. Every stove manufacturer will have a draft requirement for a stove. Normally coal and wood stoves are between .04 and .08 inches. Obviously when your chimney is undersize, temperature inside and out isn't extreme, like below 10*f. and you have a low pressure area, you aren't going to get the pressure low enough in the stove for indoor air to push oxygen into the stove. Opening a window to allow full atmospheric pressure at the stove intake may help, but a draft inducer such as a blower or electric heater in the stack may be required to force a draft.
I fired steam locomotives, and when you have steam pressure, you open a steam line that shoots steam up and out the stack to make an artificial draft through the exhaust tubes which makes a low pressure area in the firebox allowing atmospheric pressure to push through the firebed. In certain cases you need more "vacuum" than the stack or your chimney can give you. It's not you or the stove, you can have borderline conditions that won't allow enough oxygen into the stove. Same as a normally aspirated engine. When the piston goes down on the intake stroke, you only have atmospheric air pressure pushing into the intake. So at high altitude with less pressure, less power. During a storm with very low pressure, even less horsepower is available. Same as your normally aspirated stove which uses the chimney as an engine to make it go.