The stock vacuum advance distributor is connected to the carb / manifold by a small rubber joint, that in turn is mated to metal line that fits the distributor.
If the little rubber connector is deteriorated, it could allow a vacuum leak at the carb and stop the advance from working properly.
This rubber connector has a 90 degree bend. When in doubt, replace it.
Recommend: 1 x 12B2062 per Mini.
For the straight rubber connector pipe, see 12B2095
For the vacuum pipe with both connectors, see 37H4229M