There could be a foundation problem, but it could be something else. Rather than guess, having someone who knows how investigate is logical.
The symptoms do match that whatever the door is attached to is moving. It could be due to termites eating away a support beam or base plate, rather than the foundation. Or it could be that the design of the addition framing is wrong. And when something on a house moves, it can be due to failure of support from below, or addition of pressure from above, or even stress from the side.