I first try a solid flux that is inert and non-corrosive (as far as I know). It is an amber colour and does a great job.

If the wires are very stubborn then I resort to the liquid 'acid based' plumbers type flux. It REALLY works well but I always scrub the area soldered with a toothbrush dipped in either acetone or isopropyl alcohol. This prevents the acid from damaging the wires/connectors and other parts.

I have never had any long term problems using it this way.