Ideally you have two people, one to put pliers on the stubborn component and give it a gentle but constant tug, the other with desoldering braid and the iron as hot as it will go heating the pins from the other side. In the absence of two people a good fit in some sort of vice can help hold the board. Sometimes putting a bit more solder back on to the pins can help, then sucking it off with the braid again. Sometimes this makes the solder being sucked of come away together rather than leaving bits stuck in irritating places. Use leaded 60/40 or 63/37 solder if you have it. Also, there are products made which are very low temperature solder like alloys (something called chipquik I think) which can be applied like solder and then take all the actual solder away with them when you desolder, that could be something to look in to in future. But I think mainly just trying again and again with braid is the best option, and get the iron very hot, much hotter than the temperature you usually use when soldering. The other thing that might help if you have it is a flux pen, if you drip some flux on the area that may make the stubborn solder flow away more easily.