I've encountered this many times, especially with cheap Chinese connectors.
The problem seems to be that with low-quality "gold" plating you end up having all sorts of oxides, especially after some heavy soldering of a wire which heats up the banana connector, increasing its oxidation. This is very visible in Dave's connectors.
The problematic oxidation usually occurs between the multi-connect sleeve and the inner pin - depending on the design of the connector, an insertion isn't going to scratch that oxide layer away, so you have some small (measurable) resistance
Here is my simple solution - carefully solder one end of the sleeve to the inner pin (preferably the one closer to the connector as it won't increase the diameter of the tip of the connector, making it hard to insert). Use plenty of flux (preferably RMA to remove any oxidation) and just enough solder that would "wick" between the sleeve and the pin, creating a permanent connection. Don't use too much heat as it may damage the plastic handle. If you used RMA fuix, at the end, don't forget to clean the flux with alcohol so it won't cause oxidation over time.